10th Maths Ch 3 Important Questions Part 1 to score good marks in Public Exam 2027

[00:00:37]Hi students, good evening. Good evening all. Hello. Hi.

[00:00:42]How are you ma? How was the day?

[00:00:46]Yeah. Ramsh. Hi. Uh Lish. Hi Lishabi.

[00:00:50]Good evening. Good evening. Good evening all.

[00:00:54]So how was today school library? Okay.

[00:00:58]So first prep. So the finally we are going to enter chapter 3 right chapter. Yeah it was good. Yes Jum.

[00:01:11]Okay. Hi. Hi. Hi. Good evening. Good evening. Okay. So finally chapterms of the question.

[00:01:25]So chapter three single step two steps particular solutions.

[00:01:43]So formulas foreign.

[00:02:01]Okay.

[00:02:30]Okay.

[00:02:33]Yes.

[00:02:38]It is a very easy chapter only. So if you understand the concept it will be easy otherwise it is very difficult for you. Okay.

[00:02:47]So favorite.

[00:02:56]Yes.

[00:03:06]Next week.

[00:03:12]So the first question or 11th. Okay.

[00:03:36]So the variable max The father's age is six times his son's age.

[00:04:07]Obviously, so father's age is six times his son's age.

[00:04:21]Father.

[00:04:32]So father X= 6 * Y okay father six times of his son's age and next so hence 6 years So okay age of father age of father will be four times of his son age.

[00:05:26]Okay. So years.

[00:05:31]Hi. Good evening. So 6 years.

[00:05:47]Hi.

[00:05:49]Sorry.

[00:05:52]Sorry. Sorry. Sorry. I remember. Okay.

[00:05:53]Okay. Okay. Sorry.

[00:05:55]Okay.

[00:06:06]Hi Ashwin.

[00:06:08]Good evening Ashwin.

[00:06:10]Yes sir. Okay. So, x + 6 = x + = 4 * son's four times son's age.

[00:06:38]Yeah. Okay. Okay. Okay.

[00:06:42]Okay. Yes. X + 6 = So the 4 * 4 * Y.

[00:07:09]So substitute 1 in 2. Okay. So 6 y + 6 = 4 into y + 6. So 11th standard next week.

[00:07:28]Okay. Next week next.

[00:07:47]So 6 y + 6 = 4 y and 24 6 y - 4 y = 24 - 6. So 2 y= y = 18 by 2. Therefore y = 9 y= 9.

[00:08:14]Yes, everyone.

[00:08:17]Y = 9.

[00:08:20]Yes.

[00:08:28]Just hit the like button. Okay. Yes.

[00:08:32]Say yes or no.

[00:08:36]Okay.

[00:08:40]Yes. Done now.

[00:08:43]Okay.

[00:08:49]Hi. Good evening. Okay.

[00:09:04]Yes.

[00:09:06]Okay.

[00:09:18]Exercise problem= x= 6 father x= 54. Okay. So father's ages So father's age equal to 54. So you have to mention the years. Okay. So 9 years and 54 years. Okay.

[00:09:52]Okay. So son's age and the father's age.

[00:09:54]Okay.

[00:09:58]exercise.

[00:10:00]Okay. So the next question example 3.3 solve the following system of linear equation.

[00:10:13]So solve repeatable XY okay 3x - 2 y + ez = 2 yes which is equation number two equation number two. Okay.

[00:10:49]2x + 3 yus = 5 equation number two. So, so x + y + = 6 equation number three. So 11th.

[00:11:19]Okay.

[00:11:30]Yes. So you have to add one and two. So one and two.

[00:11:40]So 3x - 2 y + = 2 and 2x + 3 yus = 5.

[00:11:49]So remaining 5x + y = equation number four.

[00:12:11]So what is the next step? Next.

[00:12:16]So Hi Manosh, good evening.

[00:12:26]Equation four and five. Fifth equation.

[00:12:32]Then how can you take this fifth equation? Huh?

[00:12:44]2 and so equation 2 and so add 2 and 3 2 and 3. So 2x + 3 y 3 yus = 5 + y + = x + y + = 6. So cancel. So the remaining 3x + 4 y.

[00:13:26]Very good. Very good. Yes. Good mark.

[00:13:29]Okay. So fifth four and five. So solve four and five.

[00:13:49]So 5x + y = 7. So the fourth equation and fifth equation 3x + 4 y = 11. Fifth equation second max.

[00:14:18]Okay.

[00:14:24]Okay.

[00:14:26]Yes.

[00:14:27]Okay. So, fourth equation 28th.

[00:14:41]So, 3x + 4 y= 11.

[00:14:50]Okay. So signal H. Okay. So therefore X is equal to 17 / 17. So X is equal to the value 1.

[00:15:08]I already told you no. See basic X= 1.

[00:15:16]Yes.

[00:15:21]= you have to substitute either in fourth equation or fifth.

[00:15:41]So substitute x = 1 in.

[00:15:45]So 5x + y = 7. So 5 into 1 + y = 7. So 5 + y = 7. So y = 7 - 5. So y = awesome max.

[00:16:12]Okay. So, soute x and y value inute.

[00:16:33]Okay. So, x + y + = 6. So, 1 + 2 + = 6.

[00:16:40]So is it 3 +al 6? So is it equal to 6 - 3? So therefore is it is equal to 3. So is it equal to 3?

[00:16:51]Okay. Is it equal to three?

[00:16:56]Okay. So therefore x = 1, y = 2 and = 3.

[00:17:02]This is the solution.

[00:17:07]Max.

[00:17:11]Okay papa. So x = 1, y = 2 and = 3. So the solution yes.

[00:17:18]So have you all got the answer.

[00:17:29]Okay. So the next hit like button. Okay. Yes.

[00:17:37]So we'll move on to the next question.

[00:17:46]Okay.

[00:17:48]Example 3.5. So the same procedure solving either you have to eliminate the values or elseving method. So okay yes okay so try yourself and next example 3.7 Seven problem.

[00:18:28]Okay.

[00:18:35]Definitely you get the answer. Okay.

[00:18:39]Solve x2 - 1 = y by 6 + 1 = by 7 + 2. So which is equal to okay xx2 -1 = y by 6 + 1. So any idea?

[00:19:29]Okay. So any idea?

[00:19:39]Yes. So cross multiplication.

[00:19:47]Yes. Right. Hi Madesha.

[00:19:53]Okay.

[00:20:07]Sorry. X2. So - y 6 cross multiplication.

[00:20:15]Okay. 1 second.

[00:20:25]Yes. Okay. Done. So okay 6 y - 2 yal so 6x - 2 y = 2 into 12.

[00:20:54]Yes. So the value 24 x2 by Okay. Yes. So the whole thing so 3x - y = 3x - y - y = 12. Okay.

[00:21:59]Okay. So, xx 2 - 1 = 7 + Okay. So 7 x - 2 / 14 and 7 x - 2 = 14 into value. Good evening. Yes. So 3 into 14 into 3 what is the value?

[00:22:43]H students you guys very lazy. No. Huh?

[00:23:28]Okay, it's okay. No issues. So 7 x - 2= 4 equation number.

[00:23:42]So y 3 + 2 = Okay. First question.

[00:24:14]Yes. So listen y 3 and 2 which is equal to 13. So 2 y 3= 13 2 y + 3 = 13 into 6.

[00:24:40]Yes.

[00:24:52]78.

[00:24:54]Yes. Very good. Good. Good. So 78 number three. Okay.

[00:25:06]Okay.

[00:25:16]Okay. Y is a trick and a trick. So either you have to take one and two. One and two.

[00:25:33]Why is that again?

[00:25:47]One and two.

[00:26:02]Okay.

[00:26:04]solve 1 and 2.

[00:26:07]So first equation 3x - y = 12.

[00:26:15]Okay. So add to the second equation 7 x - 2 is it = 42.

[00:26:26]Okay. = 42 x - 7 y = So 12 into 7 what is the value 84 then you get 21 x 42 into 3 42 into 3 just solving 126. Yes. 126.

[00:27:13]Yeah. Yeah. One second. One second.

[00:27:17]So what is mean by solve?

[00:27:20]Just answer me.

[00:27:42]solve equation.

[00:27:49]XY clever.

[00:27:59]Okay. Yes. So XY unknown variable unknown.

[00:28:06]So XY equation first equation.

[00:28:21]Second equation and second.

[00:28:26]Third equation first and second equation.

[00:28:41]Okay.

[00:28:50]So - 7.

[00:28:54]Okay. So sign change - 7 y + 6 and 124 just recall 42 - 42 greater - 42 again.

[00:29:33]So again third equation - 7 y + 6 is it wait okay so - 7 y + 6 = -42.

[00:30:06]So third equation third equation equation 4 y + 6 = 78 into 3 sorry 2. So 78 into class.

[00:30:41]Okay. So 78 into 2. What is the value?

[00:30:47]156.

[00:30:50]Good. Good. So 156.

[00:31:10]Okay. Yes. Hi. Yes. Okay. Good.

[00:31:17]So now just change the sign. So signus like 4 - 11 - 11 y.

[00:31:41]Yes.

[00:31:54]- 198 198 so - 198us 11 so divide yes tell me suba mad and jana anu a hi A Saki sorry Shaki and Abi. Okay. So it is 18 minus minus get cancel. So 198.

[00:32:29]Okay. So 28 and Okay.

[00:32:39]Okay. Jessie.

[00:32:44]Okay. Yes. So y= 1 second.

[00:33:06]Okay. So 3x - y = 12 first equation y value.

[00:33:19]Okay - 18 = 12. So 3x = 12 + 18. So 3x = 30. So x= 30 / 3. So therefore x= 10. So x= 10.

[00:33:44]Yesika.

[00:33:45]Okay.

[00:33:47]Thank you. Shadow Mahadeshus 198. Okay.

[00:33:51]Done.

[00:33:53]Okay. So x= second.

[00:34:06]So 7 x - 2 = 42.

[00:34:12]Okay. So x value 10 substitute 2 is = 42. So 2 is = 42 - 70. So - 2 is equal to 42 - 70. So what is the value?

[00:34:26]Okay.

[00:34:32]Check.

[00:34:34]Okay.

[00:34:36]42 - 70. What is the value? 42 - 70 18 now 18 28 28 - 28 = - 28us you get 14 x= 10 y = 18 is it equal to 14 so this is your final Okay.

[00:35:17]Next question.

[00:35:21]Next.

[00:35:24]Okay.

[00:35:26]Yes.

[00:35:37]important questions.

[00:35:41]Okay. Already it is gay. Okay. So check why 18. Is it 14?

[00:36:06]Okay.

[00:36:15]Correct.

[00:36:17]Okay. So problem once again.

[00:36:22]So first simplify.

[00:36:49]So please it's already late.

[00:37:01]Yes. Okay.

[00:37:05]Okay.

[00:37:13]So let us assume.

[00:37:26]Yes. 1x, 1x y and 1x.

[00:37:32]Either you have to take PQ or ABC.

[00:37:42]Okay.

[00:38:02]videos.

[00:38:04]Okay.

[00:38:08]Requ.

[00:38:29]Okay.

[00:38:32]Yes.

[00:38:34]A by two cherry pa.

[00:38:36]Next 10 different.

[00:38:47]Okay.

[00:38:49]2 by n sorry 2.

[00:38:59]Okay. A by 2 b 4 c by 3. Okay. Okay.

[00:39:03]Raj. Okay. Okay. Give me some time.

[00:39:06]I will upload. Okay. So, B by 4 and sorry - C by 3 which is equal to 1 by next.

[00:39:43]A = Q by 3 sorry Q B.

[00:39:51]Okay.

[00:39:56]So, a - b by 5 + c by sorry 4 caled fraction.

[00:40:22]Okay. Mixed fraction.

[00:40:33]Yes. Mixed fraction.

[00:40:42]Yes. Sh. Okay.

[00:40:46]It is 32 by 5 15 into 32 number.

[00:41:11]So 23 2 4 3 I LC value two times. So 2 3 and again two. So three. Okay. So 2 into 2 into 3= 6 A + 3 B - 4 C 6 A + 3 B - 4 C / 12 which is equal to 1 by 4 which is equal to 1x4 11th important question already.

[00:42:16]11th important.

[00:42:26]Yes. Okay.

[00:42:31]3 - 4 C. So 12.

[00:42:38]So you get this equation.

[00:42:43]Okay.

[00:42:47]Okay.

[00:42:49]Fourth.

[00:42:51]Okay.

[00:43:03]3= B. Fifth equation.

[00:43:07]3= fifth equation.

[00:43:11]Okay. Third equation 5 a minus b and + 20 c / 5 = 32 by 15. Correct. So simplify 5 a minus b 20 c which is equal to 32x 15 into 32 32 a - 3 b and 60 c 60 c which is equal to 32 2.

[00:44:07]Okay. So, equation number six.

[00:44:28]Okay.

[00:44:41]four and six.

[00:44:44]Okay. Four and six.

[00:44:46]Fifth equation 3 a = b in fourth equation. So fourth equation 6 a + 3 b - 4 c - 4 c = 3 correct.

[00:45:16]Okay, one second.

[00:45:23]Easy problems.

[00:45:28]Okay.

[00:45:35]So, 6 into 3.

[00:45:43]Okay. So - 4 C = 3 6 A + 15 A - 4 C = 3 sorry 9. So totally 15 C = 3. Okay.

[00:46:11]Okay. Okay.

[00:46:14]Okay.

[00:46:20]So, 3 a = b. Substitute in sixth equation.

[00:46:26]15 a - 3 into 3 a + 60 c = 32. So, 15 a - 9 a + 60 c = 32.

[00:46:38]6. So 6 A + 60 C = 32.

[00:46:43]Okay.

[00:46:44]Yes.

[00:47:07]Yes. So divided by 2. Okay. 3 A + 30 C 30 C = 16. So number seven you have to find out the A value or C value.

[00:47:36]Okay.

[00:47:42]out.

[00:47:46]Okay. Yes.

[00:47:50]15 A - 4 C = 3 A + 30 C 30 C = 16 second equation. Equation seventh equation equation. So seventh equation 15 a 4 C = 3. So equation number five 150 C into what is the value 80 H.

[00:48:35]Yes.

[00:48:38]Okay.

[00:48:46]- 154 C - 77 - 77.

[00:48:56]Okay. - 77 - 77 divided by 154. What is C value here?

[00:49:06]C value 1 by 1 by 2.

[00:49:32]So substitute C value in seventh equation 15 a - 4 into 1 by 2 - 4 into 1 by 2 which is equal to 3 15 a - 2 = 3 15 a = 3 + 2 15 a = 5 so therefore a = 5 by 15 so a = 1x 3 Okay.

[00:50:03]Shortcut 1 by 15 1 by 3 1.

[00:50:22]Yes.

[00:50:26]Sorry. C value.

[00:50:28]Okay. Fourth equation fourth 6 a + 3 b - 4 c 3 b - 4 c equal to 3. Okay.

[00:50:46]So c = 1x 2 then so a = 1x 3 substitute 6 into 1x 3 + 3 b - 4 into 1x 2 = 3. So 2 + 3 b - 2 = 3 cancel. So 3 b = 3. So therefore b = 1.

[00:51:09]Okay.

[00:51:16]Okay. So answer.

[00:51:24]So final answer.

[00:51:40]What is the next step?

[00:51:44]So y= 1.

[00:52:04]So x= 3= 3. Okay. 1.

[00:52:12]So 1 = 1 it is one. Okay. 1 by= So 1= 1 by 2. So therefore is equal to two.

[00:52:30]So final answer. Yes. X= 3 Y= 1 is it is equal to two. Okay. Yes. Final answer.

[00:52:39]One second.

[00:52:55]Okay. Okay. Okay.

[00:53:02]Yes, you're right. So equal.

[00:53:34]Important question.

[00:53:52]Okay.

[00:54:07]So sum of th the first number sum of th the first number second number and twice the third number is so yes. So sum of th is the first number sum first number second number and twice the third number is second number 3x. Okay.

[00:55:00]Okay.

[00:55:04]The third number which means 2 is equal to five.

[00:55:09]Okay.

[00:55:15]Yes. It is equation number one. Okay.

[00:55:18]First number which is equal to if th number the second number is subtracted from is subtracted from sum of first number and price the third number we get. Okay.

[00:56:04]Second number three times from statement sorry first number x and the third so x + 3 is - 3 y = 2. This is your second equation test.

[00:56:38]Okay. Yes.

[00:56:42]Later on we'll do that. Okay. Yes.

[00:56:50]If the third number is if the third number is subtracted from the sum of twice the first and the second we get one. Okay.

[00:57:10]from the first which means 2x. Okay. And the second which means 3 y. Okay.

[00:57:28]minus = 1. Equation number three.

[00:57:34]Okay.

[00:57:37]Find the numbers.

[00:57:42]Okay.

[00:58:05]Okay.

[00:58:11]Okay. So, see you next class. Okay. So, GCD LCM next class.

[00:58:27]Okay. So, thank you. Thank you all. Bye.

[00:58:30]Take care. Good night. Thank you. Thank you all.