CAT Time & Work PYQs (2017–2025) | All Previous Year Questions with Solutions | CAT 2026 Quant Prep

[00:00:00]Hello everyone, welcome back to our CAT PYQ series and today I'll be talking about PYQ's of topic time and work. So let's talk about this question first. A person can complete a job in 120 days. He works alone on day one and on day two he's joined by another person who also can complete a job in exactly 120 days. So what I'm doing here I'm assuming total work as 120 units.

[00:00:28]So the efficiency of this person will be one unit per day because he completes this work in 120 days. Now on day one this person works alone that means one unit of work has been done. On day two he joined by another person who also can complete a job in exactly 120 days. So the next person efficiency is also one unit per day. So that means now the work done will be two units.

[00:01:04]On day three they are joined by another person of equal efficiency.

[00:01:13]So that means we can say now work done will be three units and so on. Like this every day a new person with the same efficiency joins the work. How many days are required to complete a job? Okay. So now how we can solve this? If you observe on the first day only one unit of work has been done.

[00:01:32]On second day two units of work has been done. On three uh day third three units of work has been done. So we can simply make a pattern out of it that on the first day one unit on the second day two unit on the third day three unit and so on.

[00:01:53]Now we have to complete 120 units of work.

[00:01:59]Now total work is 120 units. So we can understand one thing that on nth day the work done will be n units. Right? And sum of this should be equal to 120. Now from this I will try to find out the value of n. How? You can see the sum of first n natural number which is n into n + 1 by 2 is equal to 120. So this can be written as in this way 240 or you can say uh 120 into 2.

[00:02:33]Now I can use quadratic equation to find out the value of n which represent on which day this work gets completed.

[00:02:40]Right? Or you I can use some hidden trial. If you see product of two consecutive numbers. So if I break down 120 as 15 into 8.

[00:02:52]So I can say 15 into 16.

[00:02:56]So doing some smart work I can say n will be 15.

[00:03:01]That means on 15th day this work gets completed. So total days required is 15.

[00:03:09]So answer is 15.

[00:03:12]Next, Amal can complete a job in 10 days. Biml can complete it in 8 days. The first thing which comes in my mind assuming total work. So, let's do that. So, total work 40 units LCM of these two. Now we can find out the efficiency of AML that will be 40 by 10 four units and efficiency of BIML 40 by 8 five units.

[00:03:53]Amal, Bimmel and Kamill together complete a job. Job means 40 units in 4 days. So if these three persons Amal, Biml, Kamill and they worked for 4 days the work done is 40 units.

[00:04:07]Now I can put the values of A, B.

[00:04:11]Okay. So 4 + 5 + K. If you observe this got cancel out.

[00:04:20]So K comes out as one unit.

[00:04:23]Right? Now they are paid a total amount of 1,000 as remineration. If this amount is shared by them in proportion to their work. So if you observe Amal does four unit of work per day, BIML 5 and Kamill 1. So the efficiency of the these three person is 4 is to 5 is to 1 or you can say ratio of work is 4 is to 5 is to 1.

[00:04:46]So the share of Kamill will be 1 by 10 into 1,000 because this is a basic concept that uh the amount or money is divided in the ratio of their work done.

[00:05:04]Right?

[00:05:07]Next, a tank has an inlet pipe and outlet pipe. If the outlet pipe is closed, the inlet pipe fills the empty tank in 8 hours and 10 hours. The first thing which comes in my mind total work 40 units again the LCM of 8 and 10. Now use this information. If the outlet pipe is closed that means only inlet pipe is working and inlet pipe efficiency will be 40 by8 5 units.

[00:05:47]If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. That means inlet plus outlet both are working together. Now they complete this work in 10 hours. It means efficiency will be four units.

[00:06:05]Now I can put the value of inlet here to find out the efficiency of outlet.

[00:06:10]5 + outlet is equal to 4. So outlet efficiency is minus 1 unit.

[00:06:18]Next if only the outlet pip pipe is open then in how many hours the full tank becomes half. That means we have to drain 20 units and the efficiency is one unit. So time taken will be 20 by 1 that is 20 hours.

[00:06:39]Option number A.

[00:06:43]Next.

[00:06:45]A tank is fitted with pipes. Some are fillings. Test are draining. Okay. So filling pipe suppose F and draining suppose D.

[00:06:59]Okay moving on. All the filling pipes fill at the same rate and draining pipes will drain at the same rate.

[00:07:08]The empty tank gets filled in 6 hours when six filling pipe and five draining pipes are on.

[00:07:15]That means filling pipes efficiency f I think d units per now you can see six filling pipe 6 F five draining 5D and they complete the work in 6 hours.

[00:07:46]Okay.

[00:07:48]Is equal to because work is constant.

[00:07:50]Now this work is done by five filling pipes and six drain pipe in 60 hours. Right? Now obviously the value of D will be coming out as negative because drain negative work F value this got cancel out.

[00:08:14]So 6 F + 5D 50 F + 60D you can check uh this is coming out as 44 F is equal to - 55D okay to you f by d value 5 upon -4 remember f value positive DK value negative right now we can easily find out the work also work is how much put it here so 6 into 5 plus 5 into -4 into 6 right so work will be 30 - 20 that is 10 into 6 60 units Now this work is done by one drain and two filling pipes. The efficiency of 2F and one drain is put the value 2 into 5 - 4 that is 6.

[00:09:32]So time taken will be 60 by 6 that is 10 hours.

[00:09:41]Next, humans and robots can both perform a job but at different efficiency.

[00:09:49]15 humans and five robots working together take 30 days to finish the work. So 30 into 15 humans H five robots five R mandates concept we are using here you can see whereas five humans 15 robots working together takes 60 days.

[00:10:20]Now let's simplify this.

[00:10:22]cancel out two times 15 H + 5 R 10 H + 30 R so 5 H 25 R so H by R is 5 Y by 1 so I can say if H is taking five units R will be taking one unit okay H Now uh we got this thing. Next part is how many days will 15 humans working together take to finish it.

[00:11:01]Okay, let's put the value first to find out the work. So work will be 30 into 15 into 5 75 + 5 30 into 80 that is 2,400.

[00:11:19][snorts] Next in how many days will 15 humans together? So efficiency you know this.

[00:11:26]So time will be guys 2400ide by 15 into 5.

[00:11:33]Okay let's cancel this out. This is 480 and 15 3's are 30 40 sorry 45 32. So answer is 32.

[00:11:46]Next, when they work alone, B needs 25% more time to finish a job than A does. It means if A takes 4x days, 25% means 1 by 4, right? So, if I say A takes 4x days, B will take 5 X days.

[00:12:11]25% more. So, 5X, right?

[00:12:15]They two finish the job in 13 days in the following manner. A works alone till the half the job is done. So A completed 50% of work alone.

[00:12:27]A and B work together for 4 days and finally B works alone to complete the remaining 5%. So B has done 5% of work.

[00:12:37]So we can understand that A + B has done 45% of work.

[00:12:44]in 4 days right now.

[00:12:52]Can I find out 100% of work if A and B together uh do so how much time will they take? Let's find out. So 45% of work is done in 4 days.

[00:13:09]So 45 by 100 of work that is equal to 4.

[00:13:14]So work done total work done will be multiply the J. So 9 20. So 20 into 4 80 by 9.

[00:13:28]That means if A and B work together they will take how much time? 80 by 9 days.

[00:13:34]Right? Now I hope many of you know this formula that if A takes X days to complete a work, B takes Y days to complete the work. So if they together do a certain piece of work, time taken will be XY upon X + Y.

[00:13:51]Right? If you know this formula, this question becomes little bit easy. Now A is taking 4x, B is taking 5x. So 4x into 5x upon 4x + 5x and this will be equal to 80 by 9.

[00:14:09]Okay. So from this we will find out the value 20 x² upon 9x 80 by 9 got cancel out x x got cancel out. This also got cancel out. So x is equal to 4.

[00:14:26]Now what question is asking uh in how many days can B alone finish the entire job.

[00:14:33]So X value we know four 5 into 4 is 20.

[00:14:42]Next guys a water tank has inlets of two types A and B. All inlets of type A when open bring in water at the same rate.

[00:14:53]Okay.

[00:14:54]Okay. Okay, the empty tank is completely filled in 30 minutes. If 10 inlets of type A and 45 inlets of type B are open and they work for 30 minutes, 30 minutes I can say 1 by 2 half hour. Next and in 1 hour if eight inlets of type A and 18 of type B.

[00:15:23]Now let's simplify this. So two I'm sending to the right hand side.

[00:15:36]So this is 9 b is equal to 6 a right or I can say 6 a is equal to 9 b.

[00:15:47]So a by b is equal to 3x2.

[00:15:50]That means efficiency of A is three units to efficiency of B will be two units. Right?

[00:16:00]Next. So next I will find out work first. In such type of question always find out the work. So what is work?

[00:16:09]Let's put this value here or you can put it here. That will be easy. 8 into 3 + 18 into 2.

[00:16:18]So 24 + 36 60 that is work right. In how many minutes will the empty tank get completely filled if seven inlets so efficiency of seven inlets of type A and 27 of type B.

[00:16:36]Let's find out the efficiency. Let's put the value. 7 into 3 27 into 2 21 + 54 that is 75.

[00:16:51]So time taken will be because these persons or these pipes has to complete this work 60 units right so 60 by 75 hours this is an hour and to convert into minute we need to multiply by 60 now let's cancel this out 15 are 75 4 so answer is 48 minutes.

[00:17:24]Next, Romesh and Ganesh can together complete a work in 16 days. After 7 days of working together, Romesh got sick and his efficiency fell by 30%. So that means uh you can see 7 days of working together. So the work left is work left is 9 days of these two persons together. So 9 into R + G. This is your work left.

[00:17:53]Right now Romesh got sick and his efficiency fell by 30%. As a result they completed the work in 17 days instead of 16 days.

[00:18:07]observe key efficiency fell come 30%.

[00:18:13]Okay. So we can say 3R plus uh G g as it is but they are taking how much time okay sorry 30% say come over here sorry sorry this is 7 this is 7 and they are taking now how many days 17 days so the work which should be done in 9 days now they are taking 10 days one day extra let's simplify this so 9 R + 9 G 7 R + 10 G.

[00:18:49]So when we simplify this 2 R is equal to G. So R by G is equal to 1 by 2.

[00:18:57]Okay. So efficiency of this is 1 unit.

[00:19:00]Efficiency of this person is 2 unit.

[00:19:04]Now question setter is asking if Ganes had worked alone in how many days would he have completed the remaining work? So what is remaining work? First find out remaining work. 9 into 1 + 2 27 units.

[00:19:20]And this work is done by Ganesh alone.

[00:19:23]So 27 by 2 13.5.

[00:19:29]Option number C.

[00:19:36]Next. A tank is emptied every day at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. Okay. On Monday, A alone completed the and filling the tank at 8:00 p.m. So we do not know when A started the work.

[00:19:58]So what I'm doing? I do not know the efficiency of A also. So I am taking the efficiency of A as a efficiency of B as B right and the time taken by A is let's say TRS.

[00:20:11]So total work will be this click efficiency of A is A B is B and let's say time taken by A is T hours. So A into T that is total work.

[00:20:31]On Tuesday B alone completed filling the tank at 6 p.m. Okay. That means as compared to A, B is taking 2 hours less.

[00:20:41]So efficiency of B into T minus 2 on Wednesday A worked till 5 p.m. That means A tus 3 hours plus and then B worked alone from 5 p.m. to 7 p.m. So B worked for 2 hours to fill the tank. So this is total work you can see. Now I will try to find out some relation between A B right. So let's solve them individually. So first I'm targeting this these two in order to find out something then I will obviously go to this right or or you can do you can start with this also okay let's solve this a is equal to bt minus 2 b this is first equation now if I focus on this bt minus 2 b is equal to a t minus or you can I'm just focusing on this As of now, 80 is equal to 80 - 3 a + 2 b.

[00:21:52]Okay, right. This is my second equation. So, you see from this we can cancel this out. So, we can say 3 a is equal to 2 b.

[00:22:05]So, a by b I'm getting as 2x3.

[00:22:08]So we got to know the efficiency of A and B. I can say A takes up two units, B takes three units.

[00:22:18]And if I put this here, I can find out the value of T also. Let's put it here.

[00:22:23]So 2T is equal to 3T minus 6. So T is equal to 6. So we got the time also, right? So we can say the work will be 12 units.

[00:22:40]Work will be 12 units, right? 80 work is 80, right? So 2 into 6 12 units. Now at what time was the tank will on Thursday if both pipes were used simultaneously?

[00:22:54]Okay. So time taken will be 12 x 5 and in uh hours and minute if if I convert it. So I can say 2 hours 24 minute right now when did they started working?

[00:23:12]If I talk about A, A took 6 hours and A completed this work at 8:00 p.m. That means A must have started working at 2 p.m.

[00:23:26]8 - 6 2 p.m. Right?

[00:23:33]6 hours. Right? Now after 2 p.m. if these two people started working together they will take 2 hours 24 minute. So right answer will be 2 + 2 24 minute. That is option number B.

[00:23:51]Next three men.

[00:23:56]So men I'm taking capital M. Machines I'm taking small M. Eight machines can finish a job in half the time taken by so half let's say 1x2 hours or you can say 1x2 tx2 whatever you feel like three machines and eight men okay time is half right so you can See this t got cancel out.

[00:24:34]So we can say three men, eight machines, 16 men, six machines.

[00:24:43]So I can say 13 men is equivalent to three machines.

[00:24:49]Two machines. Two machines.

[00:24:54]Okay. Now question says if two machine can finish the job in 13 days. If these two machines taking 13 days to finish the work. So obviously these 13 men will also take 13 days to complete the work right because two machines is equivalent to 13 men. Simple easy question.

[00:25:19]Next.

[00:25:22]At their usual efficiency level, A and B together finish a task in 12 days. So A + B 12 days, right? Into 12. If A had worked half as efficiently as she usually does.

[00:25:37]So A by 2 plus B had worked thrice. So 3 B, right? The task would have been completed in 9 days. So we got our relation m1 d1 mandday mand days right now let's simplify this I can further cancel simplify 12 a okay I can cancel this out now I can see they say let's cancel this out by 3 okay 4 a + 4 b is equal to 3 a by 2 + 9 b so when you subtract this you will get 4 2 Right? 5 a by 2 is equal to 5 b 5 cancel out. So a by b is equal to 2 by 1. So we can say if efficiency of a is 2 unit efficiency of b will be 1 unit. Now what will be the work? Work will be 2 + 1 into 12 that is 36 units.

[00:26:43]Now question setter is asking you how many days would a take to finish the work. So time will be 36 by 2 that is 18.

[00:26:59]Next John get rupees 57 per hour for regular work. Okay. So, regular work 57 rupees per hour and overtime K gets 114 rupees per hour.

[00:27:17]If he works all together 172 hours now I do not know how many hours he has invested in regular how many hours he has invested in overtime. So what I'm doing here I'm saying suppose regular hours he took is R and overtime is O. So R + O is equal to 172. That is your first equation.

[00:27:42]And his income from overtime hours is 15% of his. Okay. So number of overtime hours is O. And the money he will be getting 1140 that is 15% of 15% 15 by 100 of income from regular hours. So 57 R.

[00:28:05]Now let's cancel this out 19 sorry 57 57 into 2 directly this uh 320.

[00:28:15]So you can say O is equal to 3 R by 40.

[00:28:21]Okay. Now if I put it here I can say R + 3 R by 40 is equal to 172.

[00:28:30]So this will be 43r by 40 is equal to 172. Now you can cancel this out by 4 I think right? So R is equal to 160. Now what is question setter asking you over time over time to you can put this here and you can say O will be 172 - 160 that is 12 so answer is 12 next anil alone can do a job in 20 days while sunil alone can do it in 40 days so what I'll be doing here the first part is total work I'm taking as 40 units 40 units total work to Anil efficiency say two units and efficiency one unit anil starts a job and after 3 days shil joins him so that means anil has worked for 3 days alone so 2 into 3 6 units is done by Anil alone okay and that means he has worked for 3 days right he has worked for 3 days Okay. After a few more days, Bimmel joins them and they together finish the job in a time I do not know if Bimmel has done 10% of the job. 10% of the job means Bimmel has done 10% of 40 that is four unit. Now this Bimmel has done this four unit. This must be done along with you know uh Anil and Sunil right he is not working alone right. So also we can understand that 30 units of work is done by Anil and Sunil.

[00:30:20]So how much time Anil and Sunil is taking. So Anil and Sunil efficiency is 2 + 1 3. So time taken by Anil and Sunil will be 30 by3 that is 10.

[00:30:33]Okay. In 10 days obviously Bimmel will also be working with them. But we do not need to worry about that in how many days Vimmel is completing his work. We need to find out the total time. So we can say Anil is working for 3 days and then the remaining 10 days they somehow managed to complete remaining work.

[00:30:52]Right? In some part B will also be working. In some part Anil and Sul will be working alone. Right? So we can say the total time will be 3 + 10 13 days.

[00:31:02]It's a very good question guys. But if you solve this in this way, you can solve this question within 30 seconds.

[00:31:10]Moving on.

[00:31:12]John takes twice as much time as Jack to finish a job. Jack and Jim together take one/ird of the time to finish the job than John takes working alone. and lots of information given to us. In how many days will Jim finish the job working alone? So how to find out this? Let's see. [snorts] So John focus John and Jack efficiency ratio is what? Two time ratio. Time ratio 2 is to1 time ratio because John is taking twice as time as compared to Jack 2 is to1. So you guys know that efficiency has a inverse relation with respect to time. Efficiency is a inversely proportional to time. Right?

[00:32:01]If someone is taking more time, he's less efficient.

[00:32:06]So inverse relation to efficiency of John and uh Jack will be what? 1 is to2.

[00:32:15]Okay. Next Jack and Jim. Jack and Jim take one/ird of the time to finish the job then John takes alone. So ratio ratio/3 1 is to 3 time ratio you got the ratio of time. So you can say efficiency ratio will be John Jack plus John Jim ratio John that will be 3 is to1 inverse relation right now if you use uh com merging of ratios easily if you can use merging of ratios easily you can easily connect if you see John is one here John is also So if I say John is doing one unit of work, Jack will be doing two unit of work and Jack plus Jim is doing three unit of work.

[00:33:24]So Jim will be doing one unit of work.

[00:33:29]Okay. So we got a relation between these three people in terms of their efficiency.

[00:33:34]Now next part is moreover uh in order to finish the job John takes 3 days more than that taken by three of them working together. Okay.

[00:33:46]If these three people are working together, so how much work they will do?

[00:33:50]Four units. And let's say they take three uh t unit sorry t hours to complete a work. Four unit of work and let's say they take hours to complete a work. Okay. The total work will be 40 and John takes 3 days more. John efficiency 1. So 1 into t + 3. Now from this we will be able to find out the value of t.

[00:34:16]So 4 t is equal to t + 3 3 t = 3 t = 1 t is equal to 1. So we got to know the time taken by these three people working together is how much? 1 hour and time taken by John will be how much t + 3. So 1 + 3 4 hours. Now question says in how many days will Jim finish the job working alone. So first of all we will try to find out the total work. So total work is four unit and gym efficiency is 1. So time taken by Jim will be four by 1 that is 4 hours. Okay. So answer of this question will be four. That's it.

[00:35:04]Right. So days answer.

[00:35:14]So everything in is in days guys. So t days.

[00:35:20]Okay.

[00:35:23]Next.

[00:35:25]A contractor agreed to construct a 6 km road in 200 days. So this question is based on contracted problem and the concept used will be m_sub_1 d1 upon w1 is equal to m_sub_2 d2 upon w2.

[00:35:41]Now let's find out the value of m_sub_1.

[00:35:43]140 persons started working right. They worked for 60 days and only 1.5 km work has been completed.

[00:35:53]Now he has hired some additional person.

[00:35:55]So suppose 140 plus x the x is the additional person he has hired and these people will work for remaining days because they have to complete this work a 200 days 60 days already used so 140 days are available and they have to complete remaining work which is 4.5 so this got cancel out three times this cancel out so 180 is equal to 140 + X X is equal to 40.

[00:36:28]So 40 additional men is required to finish this work exactly on time. Let's move on.

[00:36:38]Anu vinu Manu can complete a work alone in 15 12 and 20. So the first thing which comes in my mind total work.

[00:36:46]So total work is LCM of these. So 60 units I can clearly see that efficiency of Anu will be 4. Venu 5 Manu 3. Okay. Binu works every day. Binu is working every day. Anu works only on alternate days starting from the first day. That means Binu is working with Anu on the first day. Okay. Manu works only on the alternate days starting from the second days. Okay. Venu and Manu is working on the second days. Now they will start alternating. So what happens on third day? Vinu and Anu will be working because Venu works on every day.

[00:37:32]Next Venu and Manu will be working and so on so forth. So Venu and Anu is taking sorry doing how much work? Eight units.

[00:37:43]Sorry 9 units. 9 units and Venu and Manu 8 units 9 8 and so on like this so on right 98 98 98 the number of days needed to complete a work we have to complete 60 units so you can check 17 17 and this 17 3's are 51 + 9 60 so we took how many days 7 days because on the First day 9 unit work done. Second 8 98 989. If you take the sum you will get 60 unit which is the required work and the time taken is 7 days.

[00:38:28]Next Amar Akar and Anthony are working on a project working together. Amar and Akwar can complete a work in one year for months. Okay months about to I can say this is 12 months and this is 24 months.

[00:38:45]So let's take the LCM of 12 16 and 24. I can see 48 unit work is 48 unit.

[00:38:53]Now Ammer and Akar. So Ammer plus Akar is doing this work in 12 months. So I can see I can say four units efficiency.

[00:39:06]Akbar and Anthony Akbar and Anthony 16 months. So 48 divide by 16 3 units.

[00:39:16]Anthony and Amar complete this work in 24 months because I have converted everything in months right two units. Okay.

[00:39:30]Now I can add these three. So I can say Amar Akbar Anthony is equal to 9 by 2 units.

[00:39:42]This is twice. Okay. If you add these three you will get twice 9 units. So you can say Amar plus Akbar plus Anthony is equal to 9 by2 units.

[00:39:55]Right?

[00:39:58]Now we can find out the individual efficiencies also. If I put this value here, I will get Anthony as 0.5 units because this is guys 4.5. If you can see this is 4.5.

[00:40:12]If I put this here, I will get Ammer as 1.5.

[00:40:18]And if I put this here, I will get Akur as 2.5.

[00:40:25]Okay. Now if the person who is neither the fastest this is fastest because he's doing more work nor the slowest he's doing the least work the time in months he will take to complete a project. So we have to solve for this. So 48ide by 1.5 or you can say 3x2.

[00:40:47]So when you simplify this you will get answer as 32 months.

[00:40:53]So Amar will take 32 months to complete this work. Okay.

[00:41:00]Next part guys.

[00:41:03]Next said two pipes A and B are attached to empty water tank. Pipe A fills the tank while pipe B drains. Okay. One is doing positive, another will be doing negative. If pipe A is opened at 2 p.m.

[00:41:16]and pipe B is opened at 3 p.m. tank becomes full at 10 p.m. So pipe A must have worked for 8 hours. So 8 A pipe B must have worked for 7 hours - 7 B you can say okay or you can take plus also B will be coming out negative totally your choice. Some people takes 8 A + 7 B in that case you will be getting B value as negative. when you are taking already negative sign there you will be getting value of B as positive but you have to keep this thing in mind that B will be doing the negative work okay instead of pipe A is open at 2 p.m. pipe B is open at 4 p.m. the tank becomes full at 6 p.m.

[00:42:00]So 4 hours a b 2 hours this is your work. So simplify 4 a is equal to 5 b. So a by b is equal to 5x4.

[00:42:15]Okay. So a will be doing five units of work. B will be doing four units of drain. Okay. So total work is what?

[00:42:24]8 into 5 - 7 into 4 - 28 12 units.

[00:42:31]This is your work. Now if pipe B is not open at all the time in minutes taken to fill the tank. So A will be working alone. So time is 12 by 5. Now this is in hours we need to convert into minutes.

[00:42:50]So answer is 144 minutes.

[00:42:54]Option number C.

[00:42:59]Next.

[00:43:01]Anel can paint a house in 60 days. Biml can paint it in 84 days. So work is 420 units. The LCM of these two.

[00:43:13]An unil efficiency of unil guy is 420 by 60. 7 units.

[00:43:20]Bimmel efficiency will be 5 minutes.

[00:43:27]Anil starts painting and after 10 days so that means Anil has worked alone for 10 days. So 7 into 10 70 units of work has been done.

[00:43:38]Now Bimmel and Charu join him. So that means A B C three people are working and they complete a painting 14 more days.

[00:43:48]So they they work together for 14 days and they must be doing the remaining work. You know A has already complete is 70 units. So remaining work is 350 units which will be done by these three people.

[00:44:02]So I hope we can find out the value of A plus B plus C. Let's cancel out this.

[00:44:08]I can put this here.

[00:44:13]So the efficiency of chi uh sorry C that is charu will be 13 units t. Now what we have to find out if they are paid a total of 21,000 for the job then the share of charu proportionate to the work done by him. Let's find out the work done by a if you observe a has completed 70 units plus a has worked 40 more days. Efficiency of a is a is 7. So 7 into 14. So work done by A will be this much. Work done by Bimmel will be how much? Bimmel has worked only for 14 days. So 5 into 14.

[00:44:55]And Charu has worked for 14 days.

[00:44:58]Efficiency of Charu is 13. So 13 into 14. Now we can cancel out 14 easily. So 14 cancel out common 14 cancel out five.

[00:45:11]So you 12 year 5 13. So the ratio we are getting is 12 is to 5 is to 13. The ratio of work done by these three people is 12 is to 5 is to 13. And you need to find out the share of charu that is C.

[00:45:26]So 13 by 30 into 21,000 that is 9100.

[00:45:35]Option number B. Next, one day Rahul started a work at 9:00 a.m. Goautam joined him 2 hours later.

[00:45:46]Then they worked together and completed the work at 9:00 p.m. the same day. If you observe, Rahul has worked from 9:00 a.m. till 5:00 p.m. That means Rahul must have worked for 8 hours. And the efficiency of let's say Rahul is R. So 8 hour. Gotham worked only for 6 hours because Gotham joined 2 hours later. So plus 6 g.

[00:46:11]Okay. If both had started at 9:00 a.m.

[00:46:14]the work would have been completed 30 minutes earlier. 5 p.m. say 30 minutes earlier. Right? That means they must be working for only 7.5 hours.

[00:46:26]Let's find out the value of RNG.

[00:46:31]7.5R + 7.5g.

[00:46:37]So simplify.5 R is equal to 1.5g.

[00:46:42]So we can cancel this out. R by G will be 3 by 1. That means efficiency of RA is 3 units to Gotham key 1 unit. Now what is total work?

[00:46:55]Work will be you can put it here also 7.5 into 3 + 1 that is 30 units.

[00:47:04]So total work you've got to know that is 30 units. Now working alone the time Rahul would have taken in hours to complete the work. So Rahul efficiency is three. So time taken will be guys 30 by 3 that is 10 hours.

[00:47:22]Option number D.

[00:47:26]Next.

[00:47:29]Next says Anil can paint a house in 12 days. Vun can paint it in 16 days. Anil Vun Chandu undertake to paint a house for this and three of them together can complete a painting in 6 days. So first let's take the LCM. So total work is LCM of these two 48 units.

[00:47:48]So efficiency of Anil is four.

[00:47:52]Efficiency of Bun is three.

[00:47:56]Now when these three people Adil, Burun and Chandu work together, they complete a painting in 6 days. So I can say a + b + c into 6 is equal to 48. So 4 + 3 + c this got cancel out. Okay to c is equal to 1. C is equal to 1.

[00:48:18]Okay. Now if chandu is paid in proportion to the work done by him. So if you can see Anil efficiency of work of Anil is four, Wun is three and Chandu is one and all these people are doing work for 6 days. So you can say the ratio of work done by Anil is this, Warun is this and Chandu is this and six got cancel out.

[00:48:44]So ratio of work will be 4 is to 3 is to 1. So Chandu will be receiving Chandu share will be 1x8 of 24,000.

[00:48:54]that is 3,000. Easy question on money which is involved in time and work.

[00:49:02]Next guys, working alone the times taken by Anu Tanu Manu to complete any job are in the ratio 5 is to 8 is to 10. So you know uh efficiency is inversely proportional to time. So we can say the ratio of their efficiency will be the ratio of their efficiency will be how much? 1x 5 1x 8 1 by 10. [clears throat] Now let's take the LCM of this 40 8 54.

[00:49:41]So we got to know the efficiency of these three people. So I can say if Anu takes 8 units, Anu does 8 units of work per hour.

[00:49:53]Tanu does 5 units of work per hour and Manu does four units of work per hour.

[00:50:05]Okay, next part. they accept a job which they can finish in four days if all they work together for eight hours per day.

[00:50:15]So total work we can find out work will be what guys 4 into 8 32 and this so 4 days working 8 hours per day and the combined efficiency is 8 + 9 17 5 + 4 9 into plus yeah I think we need to solve this 32 into 17 2 are 34 17 let me check once again 17 2 are 34 3 73 is a 51. Yeah, perfect. So, we got the work also.

[00:50:51]Okay, next. What else we can do?

[00:50:55]However, if Tanu and Anu and Tanu work together for first 6 days, Anu and Tanu, we are talking about these two. So, 13 into 6 78 units of work has been done.

[00:51:09]Working 6 hours 40 minutes. Sorry, we have to consider that also. 6 hours 40 minutes means 6 2x3 hours that is 20 by3 hours. Okay guys, so 13 into 6 into 20 by3 hours this got cancel out.

[00:51:31]This is 520 units.

[00:51:35]Okay. So the remaining units says remaining okay sorry I missed out something here. This is 544 right? So remaining work is remaining work is 544 minus 520 that is 24. Okay remaining work we got to know 24. Next the number of hours that Manu will take to complete the remaining job working alone. So Manu 24x4 6 hours because this is the efficiency of Manu per hour right remaining work is 24 so that is done by Manu in 6 hours next a group of n people worked on a project they finished 35% of project by working 7 hours a day so n into 7 m1 d1 into H1 and the work completed is 35%.

[00:52:36]10 people left the group so number of people left is 10 N minus 10.

[00:52:43]The remaining people finish the rest of the project in 14 days while working 10 hours a day 65%.

[00:52:55]This got cancel out. This got cancel out. Percentage percentage gone 7 5 are 35 135 are 65 so 13 n is equal to 5 2's are 10 5 2's are 10 right 10 n minus 200 so 3 n is equal to sorry uh I must have done 10 people left a group remaining people finish the rest of the project in 14 days by working 10 hours a day. I'll have to check the calculation. Uh this is 7. This is 7.

[00:53:34]This is 7, not five. Sorry for that. H.

[00:53:39]So 13 n 14 n - 140. So n is equal to 140.

[00:53:48]So n is equal to 140.

[00:53:55]Bob can finish a job in 40 days if he works alone. Alex is twice as fast as Bob. So what I'm doing, I'm taking work.

[00:54:06]Alex is twice as fast as Bob and thrice as fast as Cole. Okay. So if you observe, Lex is twice as fast as Bob, thrice as fast as Cole. So LX is a multiple of two as well as three. So what I'm doing here, I'm taking Alex suppose six units of work.

[00:54:27]Alex does six units of work. So Bob will be doing three units of work and Cole must be doing two units of work, right?

[00:54:42]And total work will be guys total work will be since Bob can finish the job in 40 days. So 40 into 3 120 units. So we got to know total work also. Next part A and B work together on the first day.

[00:55:03]So A + B that means 9 unit of work. B and C on the second day five unit.

[00:55:13]A and C 8 unit.

[00:55:18]Then they continue to work by repeating this 3-day roster. So if you observe in 3 days how much work has been done. So 9 + 5 14 into 8 22 unit.

[00:55:29]9 + 5 14 + 8 22 units has been done in 3 days. Right?

[00:55:35]Then the total number of days Alex would have worked when the job get finished.

[00:55:38]Okay let's understand this. So in 3 days if you observe in 3 days 24 22 units of work has been done.

[00:55:47]I need to reach to 120 units. So if I multiply by five, I can say 15 days. In 15 days 110 units of work has been done.

[00:55:59]Right? Next the turn of A and B. So 16th day 9 unit of work will be done and then the turn of B and C and one unit of work has been done. But here we are looking for Alex how much sorry how many days Alex worked. So if you observe carefully in in every 3 days in the first 3 days Alex is working for 2 days. So in 15 days Alex must be working for 10 days.

[00:56:37]Right? So in 15 days Alex must be working for 10 days. Here also Alex worked because this right. So in total I can say Alex worked 10 + 11 days. So answer is 11.

[00:56:56]Next the amount of job that Amal Sunil Kamill can individually do in a day are in hermet uh sorry harmonic progression.

[00:57:06]Okay. So what I'm doing uh if I say ASK I have taken the efficiency of these three persons as ASK if ASK are in HP.

[00:57:20]So we know S is equal to 2 A K upon A + K.

[00:57:27]This is our first equation right? If three numbers are are in HP so middle number is equal to this. Now so this is efficiency we have taken care takes twice as much time as Amal to do the same amount of job. So if you see the ratio of time between Kamill and Amal Kamill and Amal is 2 is to1.

[00:57:56]Okay Kaml is taking twice time as Amal.

[00:58:00]So that means we can say efficiency of AML must be twice of Kaml because efficiency has a inverse relation. Amal efficiency is A. So and Kaml is K. So I can say A is equal to 2K.

[00:58:20]Now I can put it here.

[00:58:22]S is equal to 2 into 2K into K.

[00:58:28]This is 3K. 2k + k 3k. Now you can easily cancel out k.

[00:58:35]So you can say s is equal to 4k by 3.

[00:58:39]Okay. Now if I assume something to make my question easy what I can do you can see 4k by 3. So if I say kaml efficiency is 3 unit.

[00:58:54]So sunil s will be four unit.

[00:58:59]and Amal will be six unit.

[00:59:03]Okay, we got to know the efficiencies, right? Next, if Anna uh sorry, Amal Sunil work for 4 days, Amal and Sunil work for 4 days. So 6 + 4 10 into 4 plus of 9 days respectively. Okay, sorry for this. Uh Amal is working for 4 days. 6 into 4. Sunil is working for 9 days. 4 into 9.

[00:59:31]Kaml needs to work for 16 days to finish the remaining job. 16 into 3. So this will be work.

[00:59:39]How much? 24 + 3660 + 48 that is 108 units. This is the work.

[00:59:48]The number of days Sunil will take to finish the job working alone. Sunil efficiency is four. So time taken by Sunil will be 108 by 4 that is 27 days right days.

[01:00:01]So it's a very good question because here we are using concept of progression also.

[01:00:08]Next guys pipe A and C are filling pipes. Pipe B is a drain pipe. Pipe B empties the full tank in 1 hour less than the time taken by pipe A to fill the tank. Okay. So if I say uh A is taking a R hours B will be taking A minus 1 R and C I do not know. So see CS right when pipes A B C are turned on together the empty tank is filled in 2 hours okay pipe B will be doing a negative work we know that okay to if I use the fraction method or if I say the total work is let's say one unit if I say total work is one unit okay So a uh efficiency will be what? 1 by A.

[01:01:19]B efficiency will be what -1 A minus 1 because if it will be doing negative work C efficiency will be 1 by C and in 2 hours that means in 1 hour the work done will be 1 by 2 right because 2 hours may one unit work complete to 1 hour may 1x2 so in 1 hour their combined efficiency is this and the total work done is 1x2 we got our first equation.

[01:01:51]Similarly, if pipe B and C are turned on together when the tank is empty, pipe B is turned off after 1 hour. Then pipe C takes another 1 hour 15 minutes to fill the remaining tank. Now these two are working together. They started working together. Pipe B worked for only 1 hour.

[01:02:10]So pipe B worked for only 1 hour. So minus A minus 1. Pipe C takes another 1 hour 15 minutes. So 1 + 1 1x 4 that is 9x 4. So C worked for 9x4 hours. Okay.

[01:02:28]Okay. And they completed a work. So 9x4 C is equal to 1. Efficiency of uh C will be 1x C in 1 hour. C worked for 9x4. So that's why this this right total work is done. So yeah say what we can say we can say 9 by 4 c is equal to 1 + 1 upon a - 1. If you simplify this a - 1 a - 1 + 1 you will be getting a. So you can say 1 by c is equal to 4 a upon 9 into a - 1.

[01:03:12]Okay you got this.

[01:03:15]Now you can put this here.

[01:03:19]So 1 upon a - 1 upon a - 1 + 4 a 9 a - 1 is equal to 1 by 2.

[01:03:31]Now let's take the LCM guys. LCM is 9 a - 1.

[01:03:38]So you will be getting here what? 9 a minus 1 here you will be getting 9 a and here you will be getting 4 a into a a² 1 by 2 okay let's simplify this I can see 9 a 9 a got cancel out so - 9 + 4 a² and this is 9 a² - 9 is equal to 1 by 2 so when we simplify this we will be getting - 18 + 8 a² is equal to 9 a² - 9 so a² uh did I miss out okay this is 9 a guys this is 9 a okay 9 a h a² uh - 9 a + 18 is equal to z so from this you will get a as three as well as six right If you observe if pi P can fill the empty tank in less than 5 hours. So I cannot consider this value. This is not possible because of this statement that the value of A should be less than 5 hours. So the value of A will be three.

[01:04:56]If value of A will be three, question is asking the time taken in minutes by pipe C to fill the empty tank.

[01:05:03]So yeah here you can put here you can put mean here you can put the value of a to find out value of c. So 1x c is equal to 4 into 3 9 into 2.

[01:05:20]Okay. [snorts] So this got cancel out this got cancel out. So C is coming out as 3x2 hours or to convert into minutes we need to multiply by 60.

[01:05:33]So 90 minutes will be the right answer.

[01:05:36]So it's a very good question on time and work.

[01:05:42]Next question.

[01:05:44]Goautam and Sani working together can finish a job in 20 days. So suppose Goautam efficiency is G. Sani efficiency is S. They complete a work in 20 days.

[01:05:56]If Gotham does only 60% of work 6g and Soani must do 150% of her usual work to make up for it.

[01:06:09]Okay, we got another equation make up for it. That means they are also taking 20 days to complete a work because Gotham efficiency has down and since Gotham efficiency has gone down Sani has increase her efficiency to compensate that right now obviously from this you can find out relation between Gotham and Sani. So 4 G 5 S. So G by S is equal to 5x4.

[01:06:41]So if Gotham efficiency is five unit, Sanhani efficiency is four units.

[01:06:47]So what will be the work guys? Work will be 5 + 4 9 into 20 that is 180 units.

[01:06:57]Okay.

[01:06:58]Now then the number of days required by the faster worker to complete the job working alone. Okay. Faster worker is Goautam. So time taken will be 180 by 5.

[01:07:10]that is 36.

[01:07:17]Next, Rahul, Rakita and Gurmid working together would have taken more than 7 days to finish a job.

[01:07:26]Okay, it means what we can understand.

[01:07:28]Let's say the efficiency of this is A, this is B, this is C.

[01:07:33]So 1x a + 1x b + 1x c should be less than 1x 7 because they take more than 7 days to finish a job. So in one day they must be doing less than 1x 7 of work. Right?

[01:07:55]1x 7.

[01:07:59]If someone is taking seven days to complete a work in one day, they will be doing 1x 7 of unit. If they are taking more than 7 days, that means they must be doing less than 1x 7th of work in one day.

[01:08:14]On the other hand, Rahul and Gurm working together would have taken less than 15 days to finish the job. Okay? So that means uh Rahul a 1x a 1x c.

[01:08:29]Okay. Next. However, if they all worked together for 6 days that means these three person together worked for 6 days followed by raxita. Rakshittita means B who worked alone for three more days. So 3 by B to finish the job. The work is done. So work is one unit, right? Work is one unit.

[01:08:56]Now what we can do if Axita had worked alone on the job, the number of days she would have taken. So we need to find out the value of B.

[01:09:04]So I can see if I use these two equations smartly, I can easily find out the value of B.

[01:09:11]Right?

[01:09:14]So it's solve. So we can say 6 into 1x a + 1x b + 1x c is 1 - 3 by b right and 6 goes to left right hand side. So we get to know the value of this.

[01:09:33]We will find out the value of this. So 1 by sorry 1x a + 1 by b + 1x c is equal to 1 upon 6 1 - 3 by b right now I can put this here so 1 upon 6 1 - 3 by b is less than 1x 7.

[01:10:05]Send it to the right hand side. 1 - 3 by b 6 by 7.

[01:10:13]Okay. Now take this on the right right hand side and this on left hand side. So 1x 7 1 - 1 by 6 by 7 less than 3x b. So 1x 7 less than 3x b or you can say 3x b is greater than 1x 7.

[01:10:37]Okay.

[01:10:38]So you can simplify this and you can say 21 is greater than b or b is less than 21. So time taken by b should be less than 21 days. Now question says if Rakita had worked alone on the job okay then the number of days she would have taken to finish the job cannot be. So B cannot be 21 because what I did I let me make you understand this again. What I did here guys I have said suppose Rahul is taking A days to complete the work. B is taking suppose sorry Rakita is taking B days and Gurm is taking suppose C days to complete the work and together they are taking more than 7 days to finish the work. So if work is one unit time take uh in one day this Rahul will be doing 1x a unit and Rakshittita will be doing 1x B unit Gurm will be doing 1x c unit in together they will be doing less than 1x 7. So in such a way we we were able to solve this. Now you must be wondering key what is the use of this information. Obviously this because of this I'm able to find out the minimum value of B because I will be getting a range but here luckily I got the answer from solving only these two but minimum what can be the minimum value of B so for that I need to use this part but as of now there is no requirement so let's move on to the next card.

[01:12:15]Reu would take 15 days working 4 hours per day to complete a certain task. So, Reu takes 60 hours.

[01:12:28]Sema 40 hours.

[01:12:32]Total work LCM of these two 120 units. So, Reu 3 units per hour simma 2 units per hour.

[01:12:53]Next, they decided to work together to complete this task. Sema argues to work for the double the number of hours per day as Reu. Okay. While Reu agrees to work for the double number of days as Sema. Fine. If Reu works for 2 hours per day, it means if Reu is working for 2 hours per day.

[01:13:17]So Sema is doing that work for double the number of hours. So Sema must be doing for 4 hours per day also. While Reu agrees to work for double the number of days as Sema. So suppose Sema is doing work for X days.

[01:13:36]So Reu must be doing for 2 X days.

[01:13:39]Okay.

[01:13:41]Tell you number of days Sema will take.

[01:13:43]Let's find out the value of X. We know the total work is 120 units. We know the efficiency of these people also. This is this this. So 3 units per hour they are doing 2 hours per day for 2x days. So 3 into 2 into 2x + 2 into 4 into x is equal to 120.

[01:14:06]12x + 8 x 20x is equal to 120. x is equal to 6. That's it. Answer is 6. We need to find out the number of days simma will work. Right?

[01:14:19]Right. So x is six.

[01:14:24]Next guys, Amal and Bimmel together can complete a task in 150. Biml and Sunil first step is again total work 300.

[01:14:38]Amal and Biml two units per day.

[01:14:43]Biml and Sunil three units per day. Okay.

[01:14:49]Amal start working on the task and works for 75 days. So 75 days Amal has worked.

[01:14:58]Then Biml takes over and works for 135 days. Okay. 135 days for Bimal.

[01:15:05]Finally Sunil takes over and complete the remaining task in 45 days. 45 Sunil and the total work done is 300 units.

[01:15:14]Now let's try to break down this thing to use this information. So can I write this as 75 a + 75 b + 60 b so that I can make this I can take 75 common now I will be getting a plus b.

[01:15:36]Similarly, I can write this as 45B plus 45 S and remaining 15 B is equal to 300.

[01:15:47]Right? Now 75 into 2 150 plus 45 B 45 I can take common. So B + S 45 into 3 is 135 + 15 B is equal to 300.

[01:16:04]So 15 B is equal to 15. So B is equal to 1. Now we got to know the value of B S1.

[01:16:13]We can say A is also one. We can say S is equal to 2.

[01:16:17]That's it. Okay. Next, uh if Amal had started a task alone and worked on all days, BML had worked on every second day and Sunil had worked on every third day, then the number of days required to complete a task would have been. Let's find out.

[01:16:35]So on the first day uh Amal is working that is on the first day I can say Amal is doing first one unit. On the second day uh Bimmel also started working. So Amal plus Biml 2 unit. On the third day third day Sunil comes into picture. So Amal plus Sun uh that is three unit. on the fourth day.

[01:17:02]Fourth day because every second day BMIL works. So two unit on the fifth day only Amal will be working because two or three multiple five right and on the sixth day on the sixth day I'm four unit right let me check this I hope I have not done any mistake yeah perfectly fine okay so we got a pattern now if you try to think on The seventh day. On the seventh day, one unit. On the eighth day, two unit because multiple of two.

[01:17:44]On the ninth day, three unit multiple of three. Right? Because on every 3 days, Sunil comes into picture. Right? On the 10th day, multiple of two. So, Bimmel comes into picture along with Anil, right? Anil and Amal, sorry. So, two unit and so on. So we can generalize and we can say for every 6 days in every 6 days they must be doing how much work? 5 to 7 13 unit and we have to complete 300. So nearest multiple of 13 to 300 13 2's are 26 13 3's are right 23.

[01:18:28]So 6 into 23 is uh how many days? 138 days and this is 299 I think 13 into 23 13 are 39 132 are 299.

[01:18:49]So in 138 days 299 unit of work has been done. So that means one unit is left. So again the turn comes of amal. You can see after every 6 days we again start from this. So on the 139th day our work will be completed. So that's why the answer is 139th. It's a very good question which was asked in CAT 24.

[01:19:14]Next Sam can complete a job in 20 days when working alone. Moit is twice as fast as Sam and twice as fast as AA in the same job. So what I'm taking mo as 6 unit multiple of two as well as three sam as three unit as 2 unit right Sam can complete so total work we can find out total work will be 20 into three guys 60 units right they undertake a job with an arrangement where Sam and Mohit work together on the first day so Sam and Mohit so nine unit of work on the first day Sam and aa on the second day Sam and aa on the second day so five unit of work on second day Moit and aa on the third day 8 unit of work on the third day and this 3-day pattern is repeated till the work get completed so you can see I can do it manually also so how much is this uh 9 + 5 14 + 8 22 so 22 22 44 4 44 Okay, wait just a second. This is 9 8 13 22 for 22 + 22 44 again 44 + 14 I'm getting only 58. So that means I need two units of work also. Okay. Then the total fraction of work done by Sam.

[01:20:43]Fine. Now Sam where Sam is working. So we have to find out that Sam is working on the first day. Sam is working on the second day. Sam is working on this day, this day, this day and this day. Right?

[01:20:56]So Sam is working for 6 days. And the efficiency of Sam is three.

[01:21:03]So the work done by Sam will be 18 units with respect to total that is 60 because Sam worked for six days here, here, here, here, here, here. Right?

[01:21:15]So let's cancel out this by six. I can say 3x 10. Option number B.

[01:21:27]Next question guys. Team ABC consist of A five members, B8, C 10 members respectively such that every member within team is equally productive.

[01:21:45]Working separately, team ABC can complete a certain job in 40 hours. So, okay, they are taking 40 hours, they are taking 50 hours and they are taking 4 hours. So let's take total work. Let's say total work is 200 units.

[01:22:04]Total work is 200 units.

[01:22:08]So if you observe these five members complete this work in 40 hours, right?

[01:22:15]So I can say uh these five members doing five unit of work per hour.

[01:22:24]These eight member complete this work in 50 hours.

[01:22:30]So four unit of work per hour.

[01:22:36]These 10 member complete this work in 4 hours. So 50 units per hour.

[01:22:45]Now these are the combined efficiency.

[01:22:47]Now we can find out the individual efficiency or also every member of team A. So member key efficiency 1 unit 1 by 2 you five.

[01:23:04]Okay. Next two members from team A, three members from team B and one member from team C together start a work and member from team C leaves after 23 hours. That means these three uh combinations of people worked for 23 hours. So 23 into two members from team A. So 2 into 1 efficiency is one of each member belongs to team A 3 into 1 by 2 and member from team C 5 into uh one member right 5 into 1.

[01:23:46]Let's simplify this. 23 into 7 + 10.5, right? 10.5 1.5. Oh, sorry. Sorry, sorry.

[01:24:03]Uh, it's 3x 2 + 7 how much? 14 17 by 2.

[01:24:12]17 by 2.

[01:24:15]So how much this will be? 17 3's are 51 1 5 17 2 are 34 + 5 39 that is 195.5 Let me check the calculation also once again 5 + 2 7 + 3x 2 7 2 14 + 3 17 x 2 17 3's are 515 17 2's are 34 yeah 195.5 195.5 work has been done unit of work has been The number of additional members from team B would be required to replace the member from team C to finish the job in the next 1 hour. Now we are left with only 1 hour. You know these uh two members from team A will be working and they will be doing two unit of work.

[01:25:03]Also the efficiency of these person is one half unit. Okay. So plus two also add.

[01:25:13]So we are left with 197.5 we are have completed. So we are [snorts] left with 2.5 unit of work.

[01:25:23]Okay 2.5 unit of work. Now 2.5 unit of work is done by members of team B. The efficiency of team B members is 1 by two.

[01:25:36]So we required five members from team B.

[01:25:40]How many members are present from team B? Three members. So we need two more members.

[01:25:46]So that's why answer is option number B.

[01:25:51]Next, the rate of water flow through the pipes A, B, C are in the ratio 4 is to 9 is to 36. So what I'm doing? I'm saying suppose A efficiency is 4 units.

[01:26:04]B efficiency is 9 units. C efficiency is 36 units.

[01:26:11]Okay, an empty tank can be filled up completely by pipe a 15 hours. So total work is guys 4 into 15 60 units.

[01:26:25]If all the three pipes are used simultaneously to fill up this empty tank, the time in minutes required to fill the entire tank is nearest. Now these three are working together. So time is 60 by 49 and we have to convert this in minutes because this is in r.

[01:26:47]So this is roughly how much this is 3600ide by 49. So if instead of 49 50 the answer would have been 72 right this we know 3600 / 50 is 72. So answer will definitely be more than 72 roughly 73.

[01:27:07]So approximately 73.

[01:27:14]Option number A.

[01:27:17]Next.

[01:27:19]Ankita is twice as efficient as Bin. Bin is twice as efficient than Chandan.

[01:27:25]Chandan one unit.

[01:27:28]Bipin 2 unit.

[01:27:32]Ankita four unit twice in a if all three of them start together on a job and Bipin leaves the job after 20 days.

[01:27:42]Okay. So that means these three people work for 20 days. So 20 into 7 unit plus these three combined efficiency seven.

[01:27:58]If the job got completed in 60 days that means for the remaining 40 days bin has gone so C and A will be working. So let me write this clearly so that everyone get this part clear. And for the 40 days only B and C sorry uh A and C worked or you can say this you can say in this way also some people try to solve in this way also that for 60 days A and C worked and for 20 days B worked. So totally your choice both are same thing you will be getting the same answer from both method. So 20 into 7 + 40 into 5 340 units.

[01:28:50]This is our work right now. Number of days needed by Chandan to complete the job alone. So obviously you can see time will be 340 by 1 340 days.

[01:29:08]Yeah.

[01:29:12]Next question guys and this is the okay question based on some money also. Arun Vun Tarun if working alone can complete a task in 24 21 15 days. So first of all I will take the LCM of these three.

[01:29:32]How much will be this? 2415 120 120 into 7 840.

[01:29:40]So efficiency will be what? 2435 40 and 156 uh 56.

[01:29:56]So we got to know the efficiency.

[01:29:59]Uh this Arun will be doing Arun will be doing 35 units in one day. Warun will be doing 40 units and Tun will be doing 56 units. Now they are receiving some amount of money per day.

[01:30:21]So can we find out the f uh cost per unit? So one unit cost is here roughly approximately 60 appro 60 here also 60 but this is more than 60 so I should take write it as because 35 into 6 is 2100 so roughly 61 something this is 60 what about this 56 this is less than 60 right I do not need to solve this less 60. Okay. As of now, take.

[01:31:00]Okay. On any given day, any of the workers may or may not be employed to work. Okay. If the task needs to be completed in 10 days or less, then the minimum possible amount required. So, we have to minimize the amount and we need to make sure that work is completed in 10 or less than 10 days. Okay. So obviously I will choose that person whose uh whose one unit is more effective to me because here if you see if I'm asking him to work his one unit cost is greater than 60 right about Vun cost is one unit 60 or is less than 60. So obviously I will ask him to work for me for the 10 days because maximum 10 days is allowed. So when Tarun does so 56 into 10 560 unit is completed.

[01:31:51]Now I'm left with some work that will be done by now Wun because I cannot use this because if I use this my amount will get increased. So Wun B 840 minus 560 that is 280 and efficiency of Wun is 40. So Wun will be working for 7 days.

[01:32:16]Now we have to find out the cost. So this person worked for 10 days.

[01:32:23]This person worked for only 7 days.

[01:32:27]So 216 0 0 1 168 0 0.

[01:32:32]So answer is 34,000 sorry 38,400 option number A.

[01:32:43]So that's all in this series of pq time and work ps I will be coming up with so many videos of each and every topic like quadratic equation progression suggestions comment box please put your feedback whether you like this video or not I want your feedback also so that it motivates me to work harder for you guys. So, mil next videos. Bye-bye, guys.