High level DI- DAY 60 || Variable-Based Pie Chart (Milk & Water)|| SBI & IBPS PO MAINS 2026||

[00:00:02]Hi everyone, welcome to exam ready.

[00:00:04]Today we are going to discuss a mains level DI which is based on mixture and allocation. See in the pie chart given below some values are represented directly that is either in percentage or degree. Okay. And uh this particular value is given out of the total difference between the quantity of milk and water in five different vessels that is PQRS and T. Okay. And the all variables are positive inteious like that mentioned the uh total mixture in any vessel include milk and that of the quantity of water and the quantity of milk is more than that of water is given. Okay. And what they have given here in the fourth point the total difference is given here as milk to water as 100 ml. Okay. See uh this particular p value here 2x + 2% of 100 ml will be that difference of milk and water only here in S and in Q they have mentioned in a percentage or degree form. So 50%age of 100 means it will be equal to 15 ml. Okay, that is the difference here 8 is given. Okay, if you're converting 8 by 360 into percentage means how much we will get 30%. 30% of 100 will be equal to 30 ml as the difference of milk and water available in tube. Got it? Remaining let's find it out what they have given here. The total mixture in vessel T is uh 50. So we know milk and water. This is in case of T. Okay. Milk and water equal to 50 is okay. In T what this blue uh value is representing difference between milk and water that equal to 2 Z + 2. What they have given out of which 95 ml is water. The direct value of water is given as 95 ml. Okay. So if [snorts] you are getting a two equation like this always remember the greater in order to get the greater sum the milk value will be equal to what just add it and divided by two. Okay because only two quantities there 50 z + 2 zed + 2 / 2 will be equal to 26 z + 1. Okay. Then if you need to get the smaller value that is water value means what you have to do just subtract the both 50 is - 2 Z minus 2 divided by 2 and take its average. Okay. So 48 is Z + 2 - 2 by 2 will be equal to what? 24 is Z minus 1.

[00:02:37]Now see 24 is Z -1 is the exact water level water quantity which is given here as 95. So [snorts] 24 is Z equal to 96 is Z value equal to 4. Okay. Is that equal to 4? So the milky in T will be equal to 26 Z + 1 [snorts] 26 into 4 6 4 are 24 4 2 8 10 1 4 + 1 equal to 1 5. So 1 5 is the milker and water is 95. So the difference will be equal to how much? It is 10. Okay. The difference is 10. This is regarding the 10. 10 is the difference between milk and water. So 10 is what percentage of the 100 ml that is equal to 10%. So see here 15% 10 percentage and 30%age gone. So 55%age gone. The total pie chart is representing what 100%. So 50 uh 55%age gone means remaining 45%age will be there. So 45%age [snorts] of 100 ml will be equal to what? 45 ml that will be uh for the vessels P and what R okay so 2X + 2%age of 100 will be equal to what 2X + 2 that is the quantity of um difference of milk and water in case of P okay and Y square by 100 equal to what into 100 will be equal to the difference of milk and water in case of vessel R that is Y square this value whole be equal to 45. How we got this 45? You know 45 percentage of 100 ml. Okay. So from here we will get 2x + y² equal to 43. This is first equation. Just form it. Next read the second note. The quantity of milk in vessel P and R is 100 and uh 175 ml respectively. Here milk quantity is given. The ratio of quantity of water in um vessel P to R is given here as 2 Z is to 15. We know the value of Z as four. So 2 4 are 8 8 is to 15. Okay. See here in P the total quantity is given and the water quantity is given in the ratio. Okay. So we know the difference of water in P and R separately. Okay. See here milk is 100 in case of P. Suppose this is the total quantity for P. If I'm deducting the uh what difference between milk to water that is 2x + 2. Now we will get the water quantity in P. Okay. Then the same way if you're doing it that equal to what 98 - 2x so the same way if you're doing for the water quantity of R the total milkers water available 175. Out of this if you're deducting y square we will get the water quantity of p at r which is given in the ratio 8 by 15 just to cancel it into so 4 here 49 - x okay so 49 into 10 490 uh 490 into 5 5 24 735 - 30 x no - 15x = 175 into 4 0 700 700 - 4 y² Okay. So 35 = 15x - 4 y² got it see here in the first this is the second equation right in the first equation and second equation we can form the get the value of x or y okay see here just I'm right now multiplying it with the four to make the y quantity constant okay uh [snorts] the quotient of y constant that is 4 y² um plus 8 x will be equal to 4 3's are 12 16 172. See here we have to add it then only it will get cancelled. Okay.

[00:06:42]So 23x will be equal to 27. So x value equal to 9. Okay. x= 9 means y value will be equal to what? 2 into 9 18.

[00:06:54]So y² = 43 - 18. So y value equal to roo<unk> of 43 - 18 will be equal to what? 25 root of 25 which is equal to 5.

[00:07:05]y = 5 we got. Okay. So see the water quantity uh in P is 98 - 2X. So I'm writing here uh in P see this is the blue right? Blue representing the water.

[00:07:20]Water in P will be 98 - 2X. X is equal to 9. 2 into uh 9 2 into 9 - 80. 98 - 8 19 is 80. Okay. The water is 80. So milk will be equal to how [snorts] much? 100.

[00:07:35]So the total quantity is 180. Okay. Next we don't know regarding Q. And now we know the regarding water quantity of R.

[00:07:44]Water quantity. Milk quantity of R is what? 175 ml. And the water is 175 - 25.

[00:07:51]Y square is 25. Right? [snorts] So it will be equal to 150 the total will be equal to 325.

[00:07:58]And uh see here uh anything regarding uh we know the 10 uh here the difference uh see in milk in tea it is 1.5 and water it is 95. Okay. So the total will be equal to what? Uh 200 uh 200. Okay. The difference is 10. the total will be equal to 200. So using the notes provided we find out all the variables and uh okay so let's discuss the sub question based on it. See another vessel contain 80 ml in which ratio of milk to water is 5 is to 3. Now if the whole mixture is poured into vessel Q then the ratio of milk to water will be 5 is to 3 in the final mixture Q. Okay. Then find the initial mixture in the vessel cube. See here what they said uh in a vessel contain some mixture which is in the ratio milk to water as 5 is to 3 means total is 80 unit. Okay. So 5 is to 3 means 8 unit equal to 80. So 1 unit will be equal to 10. So milk will be equal to what 50 ml and the water will be equal to 30 ml. Okay. in one no vessel but we don't know the vessel name but it is poured into vessel Q see uh any data we know regarding the QQ this is brown color representing we don't know but we only know the difference between milk and water as 30 okay so I'm taking the quantity of milk as a means the water will be equal to what milk is greater than that of water so a minus 30 will be the water quantity got it then what they said if the um if The first mix mixture vessel is added to this cube then the given ratio is in the ratio 5 is to 3. So 50 + c a divided by um 30 + a - 30 is in the ratio 5 by 3. So how much we will get 150 + 3 a = 5 a. So 2 a = 150. So a value will be equal to 75. What they ask? A equal to 75 and uh a minus 30 will be equal to this is milk equal to 75 and water equal to 75 minus 30 is what? 45. So altogether it is equal to 120. They ask to find the initial mixture in vessel Q. Got it? See the next question. Had the initial quantity of milk in S been in M. So C in vessel S purple is vessel S. We don't know the uh what milk and water quantity but we know the difference of milk and water quantity as 50. Okay. So they have given here in the question itself quantity of milk in SS uh in S the milk itself is M. Okay. And so water will be equal to what? Milk minus 50.

[00:11:01]Okay. And 30 ml of water is further added to the initial mixture to this particular initial mixture. They have added the 50 13 ml of water. Water has been added. Okay. Then the quantity of milk will be 80%age of that of the water in the final mixture. So milk by water will be in the -5 + 30 means + 50 will be equal to what? Milk is 80%age of water. So 80 by 100 which is equal to how much? 4 by 5. So 5 m = 4 m + 60. So m value will be equal to 60. What they asked find the initial ratio of milk to water in vessel? Yes s milk is 60. So then here uh 60 - 15 + 30 which is in the ratio 45. Right? So 60 is to uh 45 will be equal to how much? If you're canceling in 15, we will get here 4 is to 3. Got it? See the next question.

[00:12:04]Which of the following must be true? The ratio of quantity of water in vessel P and the quantity of milk in vessel T is 16 is to 21. [snorts] P water and Q milk. Okay. P water is what? P's water is 80. Uh then T milk is not 5. P water is 80 is to 1.5 which is in the ratio if you're canceling in five 16 is to 21. So that is true. Okay. The total quantity of water in vessel P R and T is 325.

[00:12:37]Water [snorts] in P is what? 80. Okay. Then in R it is what? 150. 80 + 150 230 230 + 95.

[00:12:50]So how much it is? 325. So that also right 50%age of the total mixture in vessel P is milk uh in vessel P see here milk is 100 total quantity is 180 definitely if it is 200 means we can say it is two 50%age definitely it is not okay so only one and two follows so both one and two is our right answer okay see the next question if the uh initial mixture in U is 300 ml. So initially that particular mixture of U vessel U have 300 ml and a percentage is taken out from vessel U. Okay.

[00:13:35]And it is poured into vessel R then the quantity of milk and water in the final mixture of vessel R will be 275 ml and 200 ml respectively. See here uh okay see in vessel R anything we know yes in vessel R milk milk is 175 [snorts] vessel R this is case of vessel R this is in case of U okay vessel R M it is 175 and the water is what [clears throat] 150 okay and see in this to this particular R uh the vessel U that initial mixture of this U certain percentage is taken out Right? That taken out uh quantity has been added to this particular R. Then the final mixture contains 275 ml milk and 200 ml water. So what quantity of water is been added to this particular mixture. This is the final mixture and this was the initial mixture of R. Okay. So 100 ml milk and 50 ml water has been added. Got it? So 150 ml has been added. This 150 ml is taken from what? 300 ml. Okay. So they asked they given certain percentage like that.

[00:14:54]So we have to find this a percentage. So a percentage will be equal to how much equal to 50%age. Got it. And what they said the initial ratio of milk to water in the vessel U was B is to C. See here milk and water has been taken uh whatever value it has been there which is taken in the same ratio only. So the ratio of milk and water will be equal to what 2 is to 1. So a value will be 2 and b value will be equal to 1. Okay. So what they ask to find a divided by b by c b by c. So 50 divided by 2 into 1 which will be equal to 25. Got it? See the next question. If 10%age is taken out from uh tea vessel T and it is replaced with a certain amount of water then the quantity of milk and water in the final mixture of tea will be 9450 ml and 9450 ml sorry 89.50 ml find the quantity of water that was replaced. See here uh initially in tea how much does it has?

[00:16:02]Milk it contain 105 and water milk it 105 and water is 95. Okay 10% is taken out. So 10 percentage of 105 will be equal to what? 10.5 if we are deducting from this 10.5 is taken out. 105 if we are deducting how much we will get 94.5.

[00:16:24]Okay see uh the quantity of milk is 94.5. that is correctly taken. Okay.

[00:16:30]From this 95 10% is gone means now it will be equal to what? 4 uh 84.5.

[00:16:39]Okay. But they have given the final quantity of water as 89.5 because they said after removal certain amount of water has been added. So there is no change in the milk. Okay. So how much is the amount added? amount added will be equal to uh five ml. See to this four five is been added right. So how much we will get the quantity of milk added will be equal to five. See uh [clears throat] 14 85 sorry. So this will be four 4 ml. Okay. Both option five and four is the just um if you are subtracting carefully subtract. Okay. So if you have any doubt in this particular DI you can ask. Okay. Make use of our exam rally PDF course and the videos available. Okay. Thank you.