Elimination Method PYQs
Class 10 Previous Year Questions (2014 – 2026)
Topic Overview
Elimination is often the fastest algebraic method for solving linear systems. It is the preferred method for most complex word problems involving speed-distance-time, upstream-downstream, and unit price calculations.
Q1
2025
00:00
Solve algebraically: $30x + 44y = 19$ and $40x + 55y = 13$
Multiply Eq 1 by 4 and Eq 2 by 3:
$120x + 176y = 76$
$120x + 165y = 39$
Subtracting: $11y = 37 \Rightarrow y = 37/11$.
Substitute $y$: $x = -43/10$.
Ans: $x = -4.3, y = 3.36$
Q2
2022
00:00
Coach buys 4 bats and 1 ball for ₹2050. Later buys 3 bats and 2 balls for ₹1600. Find cost of each bat and ball.
Let bat = $x$, ball = $y$.
$4x + y = 2050$
$3x + 2y = 1600$
Multiply Eq 1 by 2: $8x + 2y = 4100$.
Subtract Eq 2: $5x = 2500 \Rightarrow x = 500, y = 50$.
Ans: Bat = ₹500, Ball = ₹50
Q3
2022
00:00
Solve: $2x + 3y = 11$ and $2x - 4y = -24$. Hence find $m$ for which $y = mx + 3$.
Subtracting: $7y = 35 \Rightarrow y = 5, x = -2$.
$5 = m(-2) + 3 \Rightarrow m = -1$.
Ans: $x = -2, y = 5, m = -1$
Q4
2021
00:00
Solve: $101x + 102y = 304$ and $102x + 101y = 305$
Add: $x + y = 3$. Subtract: $x - y = 1$.
Adding: $2x = 4 \Rightarrow x = 2, y = 1$.
Ans: $x = 2, y = 1$
Q5
2024
00:00
Two people 16 km apart walk simultaneously. Walking towards each other they meet in 2 h; same direction they meet in 8 h. Find their speeds.
Let speeds be $u$ and $v$.
$2(u+v) = 16 \Rightarrow u+v = 8$
$8(u-v) = 16 \Rightarrow u-v = 2$
Solving: $u=5, v=3$.
Ans: 5 km/h and 3 km/h
Q6
2023
00:00
In $\triangle ABC$, $\angle A = x^{\circ}$, $\angle B = (3x-2)^{\circ}$, $\angle C = y^{\circ}$. Also $\angle C - \angle B = 9^{\circ}$. Determine all three angles.
$4x + y = 182, y - 3x = 7$.
Subtracting: $7x = 175 \Rightarrow x = 25$.
Angles: 25°, 73°, 82°.
Ans: 25°, 73°, 82°
Q7
2021
00:00
5 pencils and 7 pens cost ₹50; 7 pencils and 5 pens cost ₹46. Find cost of 1 pencil and 1 pen.
$5x + 7y = 50, 7x + 5y = 46$.
Add: $x+y=8$. Subtract: $y-x=2$.
Solving: $y=5, x=3$.
Ans: Pencil = ₹3, Pen = ₹5
Q8
2019
00:00
Solve: $(a-b)x + (a+b)y = a^2 - 2ab - b^2$ and $(a+b)(x+y) = a^2 + b^2$
Eq 2: $(a+b)x + (a+b)y = a^2 + b^2$.
Subtract: $[(a+b)-(a-b)]x = 2ab + 2b^2 \Rightarrow x = a+b, y = -2ab/(a+b)$.
Ans: $x=a+b, y=-2ab/(a+b)$
Q9
2016
00:00
Boat: 32 km upstream + 36 km downstream = 7 hrs. Also 40 km up + 48 km down = 9 hrs. Find speed of boat and stream.
Let $1/(x-y)=a, 1/(x+y)=b$.
$32a+36b=7, 40a+48b=9$.
Solving: $a=1/8, b=1/12 \Rightarrow x-y=8, x+y=12 \Rightarrow x=10, y=2$.
Ans: Boat = 10 km/h, Stream = 2 km/h
Q10
2015
00:00
Solve: $47x + 31y = 63$ and $31x + 47y = 15$
Add: $x+y=1$. Subtract: $x-y=3$.
Solving: $x=2, y=-1$.
Ans: $x=2, y=-1$
Q11
2023
00:00
Two schools P and Q award prizes for Hockey (₹x) and Cricket (₹y).
School P: 5 hockey + 4 cricket students = ₹9,500
School Q: 4 hockey + 3 cricket students = ₹7,370
School P: 5 hockey + 4 cricket students = ₹9,500
School Q: 4 hockey + 3 cricket students = ₹7,370
$5x + 4y = 9500, 4x + 3y = 7370$.
Solving: $x=980, y=1150$.
Ans: x=₹980, y=₹1150
Q12
2020
00:00
Man travels 370 km: 250 km by train + rest by car = 4 hrs. 130 km by train + rest by car = 4 h 18 min. Find speeds of train and car.
$250/x + 120/y = 4, 130/x + 240/y = 4.3$.
Solving: $x=100$ km/h, $y=80$ km/h.
Ans: Train = 100 km/h, Car = 80 km/h
Q13
2019
00:00
Places A and B are 100 km apart. Two cars start simultaneously. Same direction: meet in 5 h. Towards each other: meet in 1 h. Find their speeds.
$x+y = 100, x-y = 20$.
Solving: $x=60, y=40$.
Ans: 60 km/h and 40 km/h
Q14
2018
00:00
A train at uniform speed: 10 km/h faster $\Rightarrow$ 2 hours less. 10 km/h slower $\Rightarrow$ 3 hours more. Find distance covered.
$5t-x=10, 3x-10t=30$.
Solving: $t=12, x=50, D=600$.
Ans: 600 km
Q15
2026
00:00
PASSAGE: Nidhi and Riddhi visited a mela. Nidhi: 3 rides on Giant Wheel + 5 on Toy Train = ₹14. Riddhi: 5 rides on Giant Wheel + 3 on Toy Train = ₹18.
(i) Form a pair of linear equations.
(ii) Cost per ride for Giant Wheel.
(iii) (a) Cost per ride for Toy Train and verify. OR (b) Nidhi's cost for 2 rides on each.
(i) Form a pair of linear equations.
(ii) Cost per ride for Giant Wheel.
(iii) (a) Cost per ride for Toy Train and verify. OR (b) Nidhi's cost for 2 rides on each.
(i) $3x+5y=14, 5x+3y=18$.
(ii) $x=3$ (Giant Wheel).
(iii) $y=1$ (Toy Train). (b) ₹8.
Q16
2025
00:00
PASSAGE: Quiz competition. +4 for correct, -1 for wrong. Team A: 10 questions, score 28. Team B: 12 questions, score 38. Both answered all.
(i) Write equations for each team.
(ii) Correct answers for each team.
(iii) (a) Team A score if 15 questions (same ratio). OR (b) Total correct by both = 13; find each team's correct answers.
(i) Write equations for each team.
(ii) Correct answers for each team.
(iii) (a) Team A score if 15 questions (same ratio). OR (b) Total correct by both = 13; find each team's correct answers.
(i) Team A: $4c-w=28, c+w=10$. Team B: $4c-w=38, c+w=12$.
(ii) Team A=7, Team B=10.
Q17
2024
00:00
PASSAGE: Ramesh buys 2 type-A bonds + 1 type-B bond = ₹700 annual interest. Suresh buys 1 type-A + 2 type-B = ₹800.
(i) Form pair of linear equations.
(ii) Annual interest for each bond type.
(iii) (a) Geeta buys 3 of each — total interest? OR (b) If total from 1 of each = ₹500, find values.
(i) Form pair of linear equations.
(ii) Annual interest for each bond type.
(iii) (a) Geeta buys 3 of each — total interest? OR (b) If total from 1 of each = ₹500, find values.
(i) $2x+y=700, x+2y=800$.
(ii) $x=200, y=300$.
(iii) (a) ₹1500.
Q18
2023
00:00
PASSAGE: School P: 4 honesty (₹x) + 3 hardwork (₹y) prizes = ₹7000. School Q: 3 honesty + 5 hardwork = ₹8000.
(i) Represent algebraically.
(ii) Price of Honesty award.
(iii) (a) Price of Hardwork + total for 2 students each. OR (b) Which prize amount is more and by how much?
(i) Represent algebraically.
(ii) Price of Honesty award.
(iii) (a) Price of Hardwork + total for 2 students each. OR (b) Which prize amount is more and by how much?
(i) $4x+3y=7000, 3x+5y=8000$.
(ii) x=₹800, y=₹1400.
Solve algebraically: $30x + 44y = 19$ and $40x + 55y = 13$
Multiply Eq 1 by 4 and Eq 2 by 3:
$120x + 176y = 76$
$120x + 165y = 39$
Subtracting: $11y = 37 \Rightarrow y = 37/11$.
Substitute $y$: $x = -43/10$.
Ans: $x = -4.3, y = 3.36$
Q2
2022
00:00
Coach buys 4 bats and 1 ball for ₹2050. Later buys 3 bats and 2 balls for ₹1600. Find cost of each bat and ball.
Let bat = $x$, ball = $y$.
$4x + y = 2050$
$3x + 2y = 1600$
Multiply Eq 1 by 2: $8x + 2y = 4100$.
Subtract Eq 2: $5x = 2500 \Rightarrow x = 500, y = 50$.
Ans: Bat = ₹500, Ball = ₹50
Q3
2022
00:00
Solve: $2x + 3y = 11$ and $2x - 4y = -24$. Hence find $m$ for which $y = mx + 3$.
Subtracting: $7y = 35 \Rightarrow y = 5, x = -2$.
$5 = m(-2) + 3 \Rightarrow m = -1$.
Ans: $x = -2, y = 5, m = -1$
Q4
2021
00:00
Solve: $101x + 102y = 304$ and $102x + 101y = 305$
Add: $x + y = 3$. Subtract: $x - y = 1$.
Adding: $2x = 4 \Rightarrow x = 2, y = 1$.
Ans: $x = 2, y = 1$
Q5
2024
00:00
Two people 16 km apart walk simultaneously. Walking towards each other they meet in 2 h; same direction they meet in 8 h. Find their speeds.
Let speeds be $u$ and $v$.
$2(u+v) = 16 \Rightarrow u+v = 8$
$8(u-v) = 16 \Rightarrow u-v = 2$
Solving: $u=5, v=3$.
Ans: 5 km/h and 3 km/h
Q6
2023
00:00
In $\triangle ABC$, $\angle A = x^{\circ}$, $\angle B = (3x-2)^{\circ}$, $\angle C = y^{\circ}$. Also $\angle C - \angle B = 9^{\circ}$. Determine all three angles.
$4x + y = 182, y - 3x = 7$.
Subtracting: $7x = 175 \Rightarrow x = 25$.
Angles: 25°, 73°, 82°.
Ans: 25°, 73°, 82°
Q7
2021
00:00
5 pencils and 7 pens cost ₹50; 7 pencils and 5 pens cost ₹46. Find cost of 1 pencil and 1 pen.
$5x + 7y = 50, 7x + 5y = 46$.
Add: $x+y=8$. Subtract: $y-x=2$.
Solving: $y=5, x=3$.
Ans: Pencil = ₹3, Pen = ₹5
Q8
2019
00:00
Solve: $(a-b)x + (a+b)y = a^2 - 2ab - b^2$ and $(a+b)(x+y) = a^2 + b^2$
Eq 2: $(a+b)x + (a+b)y = a^2 + b^2$.
Subtract: $[(a+b)-(a-b)]x = 2ab + 2b^2 \Rightarrow x = a+b, y = -2ab/(a+b)$.
Ans: $x=a+b, y=-2ab/(a+b)$
Q9
2016
00:00
Boat: 32 km upstream + 36 km downstream = 7 hrs. Also 40 km up + 48 km down = 9 hrs. Find speed of boat and stream.
Let $1/(x-y)=a, 1/(x+y)=b$.
$32a+36b=7, 40a+48b=9$.
Solving: $a=1/8, b=1/12 \Rightarrow x-y=8, x+y=12 \Rightarrow x=10, y=2$.
Ans: Boat = 10 km/h, Stream = 2 km/h
Q10
2015
00:00
Solve: $47x + 31y = 63$ and $31x + 47y = 15$
Add: $x+y=1$. Subtract: $x-y=3$.
Solving: $x=2, y=-1$.
Ans: $x=2, y=-1$
Q11
2023
00:00
Two schools P and Q award prizes for Hockey (₹x) and Cricket (₹y).
School P: 5 hockey + 4 cricket students = ₹9,500
School Q: 4 hockey + 3 cricket students = ₹7,370
School P: 5 hockey + 4 cricket students = ₹9,500
School Q: 4 hockey + 3 cricket students = ₹7,370
$5x + 4y = 9500, 4x + 3y = 7370$.
Solving: $x=980, y=1150$.
Ans: x=₹980, y=₹1150
Q12
2020
00:00
Man travels 370 km: 250 km by train + rest by car = 4 hrs. 130 km by train + rest by car = 4 h 18 min. Find speeds of train and car.
$250/x + 120/y = 4, 130/x + 240/y = 4.3$.
Solving: $x=100$ km/h, $y=80$ km/h.
Ans: Train = 100 km/h, Car = 80 km/h
Q13
2019
00:00
Places A and B are 100 km apart. Two cars start simultaneously. Same direction: meet in 5 h. Towards each other: meet in 1 h. Find their speeds.
$x+y = 100, x-y = 20$.
Solving: $x=60, y=40$.
Ans: 60 km/h and 40 km/h
Q14
2018
00:00
A train at uniform speed: 10 km/h faster $\Rightarrow$ 2 hours less. 10 km/h slower $\Rightarrow$ 3 hours more. Find distance covered.
$5t-x=10, 3x-10t=30$.
Solving: $t=12, x=50, D=600$.
Ans: 600 km
Q15
2026
00:00
PASSAGE: Nidhi and Riddhi visited a mela. Nidhi: 3 rides on Giant Wheel + 5 on Toy Train = ₹14. Riddhi: 5 rides on Giant Wheel + 3 on Toy Train = ₹18.
(i) Form a pair of linear equations.
(ii) Cost per ride for Giant Wheel.
(iii) (a) Cost per ride for Toy Train and verify. OR (b) Nidhi's cost for 2 rides on each.
(i) Form a pair of linear equations.
(ii) Cost per ride for Giant Wheel.
(iii) (a) Cost per ride for Toy Train and verify. OR (b) Nidhi's cost for 2 rides on each.
(i) $3x+5y=14, 5x+3y=18$.
(ii) $x=3$ (Giant Wheel).
(iii) $y=1$ (Toy Train). (b) ₹8.
Q16
2025
00:00
PASSAGE: Quiz competition. +4 for correct, -1 for wrong. Team A: 10 questions, score 28. Team B: 12 questions, score 38. Both answered all.
(i) Write equations for each team.
(ii) Correct answers for each team.
(iii) (a) Team A score if 15 questions (same ratio). OR (b) Total correct by both = 13; find each team's correct answers.
(i) Write equations for each team.
(ii) Correct answers for each team.
(iii) (a) Team A score if 15 questions (same ratio). OR (b) Total correct by both = 13; find each team's correct answers.
(i) Team A: $4c-w=28, c+w=10$. Team B: $4c-w=38, c+w=12$.
(ii) Team A=7, Team B=10.
Q17
2024
00:00
PASSAGE: Ramesh buys 2 type-A bonds + 1 type-B bond = ₹700 annual interest. Suresh buys 1 type-A + 2 type-B = ₹800.
(i) Form pair of linear equations.
(ii) Annual interest for each bond type.
(iii) (a) Geeta buys 3 of each — total interest? OR (b) If total from 1 of each = ₹500, find values.
(i) Form pair of linear equations.
(ii) Annual interest for each bond type.
(iii) (a) Geeta buys 3 of each — total interest? OR (b) If total from 1 of each = ₹500, find values.
(i) $2x+y=700, x+2y=800$.
(ii) $x=200, y=300$.
(iii) (a) ₹1500.
Q18
2023
00:00
PASSAGE: School P: 4 honesty (₹x) + 3 hardwork (₹y) prizes = ₹7000. School Q: 3 honesty + 5 hardwork = ₹8000.
(i) Represent algebraically.
(ii) Price of Honesty award.
(iii) (a) Price of Hardwork + total for 2 students each. OR (b) Which prize amount is more and by how much?
(i) Represent algebraically.
(ii) Price of Honesty award.
(iii) (a) Price of Hardwork + total for 2 students each. OR (b) Which prize amount is more and by how much?
(i) $4x+3y=7000, 3x+5y=8000$.
(ii) x=₹800, y=₹1400.