CBSE Class 8 Mathematics Linear Equations in Two Variables MCQs Set 18

Download CBSE MCQs for Class 8 Mathematics: Linear Equations in Two Variables

Access targeted multiple-choice questions for Linear Equations in Two Variables designed to align with the latest CBSE academic syllabus for Class 8 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Chapter-wise Objective Questions: Linear Equations in Two Variables

View or download the dedicated Linear Equations in Two Variables MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: The cost of a notebook is twice the cost of a pen. If x is the cost of a notebook and y is the cost of a pen, the linear equation in two variables is
(a) x = −2y
(b) x = 4y
(c) x = 2y
(d) x = 3y
Show Answer & Explanation

Answer: (c) x = 2y

Explanation:
1. Notebook cost = 2 × pen cost, so x = 2y.

Teacher's Note:
1. Translate the words directly into an equation.
2. Check with y = 5, x = 10.

Question 2: The taxi fare in a city is Rs. 8 for the first kilometre and Rs. 5 per km for the subsequent distance. If the distance covered is x km (x ≥ 1) and the total fare is Rs. y, the linear equation is
(a) y = 5x + 8
(b) y = 5x − 3
(c) y = 8x + 5
(d) y = 5x + 3
Show Answer & Explanation

Answer: (d) y = 5x + 3

Explanation:
1. Fare = 8 + 5(x − 1) = 5x + 3.
2. Check: x = 1 gives y = 8.

Teacher's Note:
1. Charge the first km separately, then (x − 1) km at Rs. 5.
2. Test with x = 1 and x = 2 (fare 13).

Question 3: Yamini and Fatima together contributed Rs. 100 to a relief fund. If their contributions were Rs. x and Rs. y, the linear equation is
(a) x − y = 100
(b) x + y = 50
(c) x + y = 100
(d) xy = 100
Show Answer & Explanation

Answer: (c) x + y = 100

Explanation:
1. Total contribution = x + y = 100.

Teacher's Note:
1. Sum of the two contributions is the total.
2. The equation has infinitely many solutions.

Question 4: A and B each have some oranges. A says to B, "If you give me 10 of your oranges, I will have twice the number left with you." B replies, "If you give me 10 of yours, I will have the same number as left with you." The numbers of oranges with A and B are
(a) 70 and 50
(b) 60 and 40
(c) 50 and 70
(d) 80 and 60
Show Answer & Explanation

Answer: (a) 70 and 50

Explanation:
1. Let A have a and B have b: a + 10 = 2(b − 10) and b + 10 = a − 10.
2. From the second, a = b + 20. Then b + 30 = 2b − 20, so b = 50 and a = 70.

Teacher's Note:
1. Form two equations and substitute.
2. Check: 80 = 2 × 40 and 60 = 60.

Question 5: A man has only 20 paise and 25 paise coins in his purse. If he has 50 coins in all, totalling Rs. 11.25, how many coins of each kind does he have?
(a) 20 coins of 20 paise and 30 coins of 25 paise
(b) 15 coins of 20 paise and 35 coins of 25 paise
(c) 25 coins of 20 paise and 25 coins of 25 paise
(d) 30 coins of 20 paise and 20 coins of 25 paise
Show Answer & Explanation

Answer: (c) 25 coins of 20 paise and 25 coins of 25 paise

Explanation:
1. Let there be x coins of 20 paise: 0.20x + 0.25(50 − x) = 11.25.
2. 12.5 − 0.05x = 11.25, so x = 25 and there are 25 coins of 25 paise.

Teacher's Note:
1. Value of coins = number × denomination.
2. Check: 5 + 6.25 = 11.25.

Question 6: The sum of a two-digit number and the number obtained by reversing its digits is 121, and the digits differ by 3 with the tens digit larger. The number is
(a) 65
(b) 83
(c) 47
(d) 74
Show Answer & Explanation

Answer: (d) 74

Explanation:
1. Let the digits be a (tens) and b: 11(a + b) = 121, so a + b = 11, and a − b = 3.
2. a = 7 and b = 4, so the number is 74.

Teacher's Note:
1. Number + its reverse = 11 × (sum of digits).
2. Check: 74 + 47 = 121.

Question 7: The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If both are decreased by 1, the numerator becomes half the denominator. The fraction is
(a) 3/7
(b) 4/9
(c) 5/8
(d) 4/7
Show Answer & Explanation

Answer: (d) 4/7

Explanation:
1. Let the fraction be n/d: n + d = 2d − 3, so n = d − 3.
2. n − 1 = (d − 1) / 2 gives 2d − 8 = d − 1, so d = 7 and n = 4.

Teacher's Note:
1. Form two linear equations in n and d.
2. Check: 4 + 7 = 11 = 14 − 3 and 3 / 6 = 1/2.

Question 8: Ten years ago a father was twelve times as old as his son, and ten years hence he will be twice as old as his son will be. Their present ages are
(a) Father 34 years, son 12 years
(b) Father 40 years, son 14 years
(c) Father 44 years, son 15 years
(d) Father 36 years, son 13 years
Show Answer & Explanation

Answer: (a) Father 34 years, son 12 years

Explanation:
1. f − 10 = 12(s − 10) and f + 10 = 2(s + 10).
2. Subtract: from the second f = 2s + 10, so 2s + 10 − 10 = 12s − 120, giving s = 12 and f = 34.

Teacher's Note:
1. Write both conditions as equations.
2. Check: 24 = 12 × 2 and 44 = 2 × 22.

Question 9: Reema bought x pens at Rs. 2.60 each and y greeting cards at 80 paise each. If the pens cost Rs. 12 more than the cards, the equation is
(a) 13x − 4x = 6
(b) 260x − 8y = 100
(c) 260x − 8y = 12
(d) 13x − 4y = 60
Show Answer & Explanation

Answer: (d) 13x − 4y = 60

Explanation:
1. 2.60x − 0.80y = 12.
2. Multiply by 5: 13x − 4y = 60.

Teacher's Note:
1. Keep rupees and paise in the same unit.
2. Multiplying by 5 clears the decimals.

Question 10: Which of the following is NOT a solution of 2x − 5y = 4?
(a) x = 2, y = 0
(b) x = 15, y = 6
(c) x = 7, y = 2
(d) x = 12, y = 4
Show Answer & Explanation

Answer: (b) x = 15, y = 6

Explanation:
1. (2, 0): 4 − 0 = 4. (7, 2): 14 − 10 = 4. (12, 4): 24 − 20 = 4.
2. (15, 6): 30 − 30 = 0, not 4.

Teacher's Note:
1. Substitute each pair.
2. The pair that gives a different value is not a solution.

Question 11: Two numbers are in the ratio 3 : 8 and their sum is 165. The larger number is
(a) 110
(b) 135
(c) 120
(d) 45
Show Answer & Explanation

Answer: (c) 120

Explanation:
1. Sum of parts = 11, so one part = 15.
2. Numbers: 45 and 120.

Teacher's Note:
1. Divide the sum in the given ratio.
2. Larger number = 8 × 15.

Question 12: 4 tables and 3 chairs together cost Rs. 2250, and 3 tables and 4 chairs cost Rs. 1950. The cost of 2 chairs and 1 table is
(a) Rs. 900
(b) Rs. 600
(c) Rs. 750
(d) Rs. 1050
Show Answer & Explanation

Answer: (c) Rs. 750

Explanation:
1. 4T + 3C = 2250 and 3T + 4C = 1950.
2. Subtracting: T − C = 300; adding: 7(T + C) = 4200, so T + C = 600.
3. T = 450, C = 150. So 2C + T = 300 + 450 = 750.

Teacher's Note:
1. Adding and subtracting the equations is faster than substitution.
2. Check: 1800 + 450 = 2250.

Question 13: The sum of two numbers is 35 and their difference is 13. The numbers are
(a) 24 and 11
(b) 22 and 13
(c) 23 and 12
(d) 25 and 10
Show Answer & Explanation

Answer: (a) 24 and 11

Explanation:
1. Larger = (35 + 13) / 2 = 24 and smaller = (35 − 13) / 2 = 11.

Teacher's Note:
1. Sum and difference give both numbers.
2. Check: 24 + 11 = 35.

Question 14: The sum of a two-digit number and the number formed by interchanging its digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. The number is
(a) 39
(b) 84
(c) 48
(d) 57
Show Answer & Explanation

Answer: (c) 48

Explanation:
1. 11(a + b) = 132, so a + b = 12.
2. Number + 12 = 5 × 12 = 60, so the number is 48 (digits 4 and 8, sum 12).

Teacher's Note:
1. Use number + reverse = 11 × digit sum.
2. Check: 48 + 84 = 132.

Free study material for Mathematics

Linear Equations in Two Variables Objective Questions & Solutions for Class 8 Mathematics

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FAQs

Where can I access latest CBSE Class 8 Mathematics Linear Equations in Two Variables MCQs Set 18?

You can get most exhaustive CBSE Class 8 Mathematics Linear Equations in Two Variables MCQs Set 18 for free on StudiesToday.com. These MCQs for Class 8 Mathematics are updated for the 2026-27 academic session as per CBSE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 8 material?

Yes, our CBSE Class 8 Mathematics Linear Equations in Two Variables MCQs Set 18 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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