CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 36

Practice MCQs for Class 8 Mathematics Chapter 02 Linear Equations in One Variable

Explore reliable objective questions for Chapter 02 Linear Equations in One Variable tailored for Class 8 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Access Chapter 02 Linear Equations in One Variable Questions and Solutions

Access the complete set of multiple-choice questions for Chapter 02 Linear Equations in One Variable below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: Eight less than three times a number is equal to one. Find the number.
(a) 4
(b) 3
(c) 2
(d) 9
Show Answer & Explanation

Answer: (b) 3

Explanation:
1. 3x − 8 = 1, so 3x = 9 and x = 3.

Teacher's Note:
1. Translate words to an equation first.
2. Check: 3 × 3 − 8 = 1.

Question 2: The sum of two numbers is 40. One number is 10 more than the other. The numbers are
(a) 28 and 12
(b) 25 and 15
(c) 30 and 10
(d) 20 and 20
Show Answer & Explanation

Answer: (b) 25 and 15

Explanation:
1. Let the numbers be x and x + 10: 2x + 10 = 40, so x = 15.
2. The numbers are 15 and 25.

Teacher's Note:
1. Use one variable for the smaller number.
2. Check: 25 − 15 = 10 and 25 + 15 = 40.

Question 3: A teacher said, "If you add 7 to 3 times my number, you get 31." What number did she think of?
(a) 10
(b) 7
(c) 8
(d) 9
Show Answer & Explanation

Answer: (c) 8

Explanation:
1. 3x + 7 = 31, so 3x = 24 and x = 8.

Teacher's Note:
1. Form the equation in the order the operations are described.
2. Check: 3 × 8 + 7 = 31.

Question 4: The sum of four consecutive integers is 178. The integers are
(a) 42, 43, 44, 45
(b) 41, 44, 45, 48
(c) 44, 45, 46, 47
(d) 43, 44, 45, 46
Show Answer & Explanation

Answer: (d) 43, 44, 45, 46

Explanation:
1. Let the integers be n, n + 1, n + 2, n + 3: 4n + 6 = 178, so n = 43.
2. The integers are 43, 44, 45, 46.

Teacher's Note:
1. Consecutive integers differ by 1.
2. Quick check: 178 / 4 = 44.5 is the middle.

Question 5: In a town of population 90,000, the male population is two-thirds the female population. The male population is
(a) 54,000
(b) 45,000
(c) 36,000
(d) 30,000
Show Answer & Explanation

Answer: (c) 36,000

Explanation:
1. Let females = f: f + (2/3)f = 90000, so (5/3)f = 90000 and f = 54000.
2. Males = 90000 − 54000 = 36,000.

Teacher's Note:
1. Express males in terms of females.
2. Check: 2/3 of 54000 = 36000.

Question 6: Ram is half his father's age now. Ten years ago he was 20 years younger than his father. Their present ages are
(a) Ram 25 years, father 50 years
(b) Ram 20 years, father 40 years
(c) Ram 10 years, father 20 years
(d) Ram 15 years, father 30 years
Show Answer & Explanation

Answer: (b) Ram 20 years, father 40 years

Explanation:
1. Let Ram be x and father 2x. The age difference is always x, so x = 20.
2. Ram is 20 and father is 40.

Teacher's Note:
1. The difference in ages never changes with time.
2. Check: ten years ago they were 10 and 30.

Question 7: The sum of x and x + 3 is 15. The value of x is
(a) 12
(b) 10
(c) 6
(d) 8
Show Answer & Explanation

Answer: (c) 6

Explanation:
1. x + (x + 3) = 15, so 2x = 12 and x = 6.

Teacher's Note:
1. Combine like terms.
2. Check: 6 + 9 = 15.

Question 8: Divide x by 4 and then add 13. If the result is 33, find x.
(a) 20
(b) 113
(c) 46
(d) 80
Show Answer & Explanation

Answer: (d) 80

Explanation:
1. x / 4 + 13 = 33, so x / 4 = 20 and x = 80.

Teacher's Note:
1. Undo the operations in reverse order.
2. Check: 80 / 4 + 13 = 33.

Question 9: The length of a rectangle is (p + 3) cm and its breadth is (2p − 5) cm. If its perimeter is 26 cm, find the area of the rectangle in cm².
(a) 56
(b) 13
(c) 40
(d) 48
Show Answer & Explanation

Answer: (c) 40

Explanation:
1. Perimeter: 2[(p + 3) + (2p − 5)] = 26, so 3p − 2 = 13 and p = 5.
2. Length = 8 cm and breadth = 5 cm, so area = 40 cm².

Teacher's Note:
1. Half the perimeter equals length plus breadth.
2. Find p first, then the area.

Question 10: The sum of two consecutive whole numbers is 11. If the smaller number is n, the correct equation is
(a) n + n + 1 = 11
(b) 2n − n = 11
(c) 2n = 11
(d) n + n − 1 = 11
Show Answer & Explanation

Answer: (a) n + n + 1 = 11

Explanation:
1. The next whole number is n + 1.
2. So n + (n + 1) = 11, which gives n = 5 (numbers 5 and 6).

Teacher's Note:
1. The larger consecutive number is n + 1.
2. The two numbers are 5 and 6.

Question 11: Given that 2m − 5 = 10 − m, find m.
(a) 2
(b) 4
(c) 3
(d) 5
Show Answer & Explanation

Answer: (d) 5

Explanation:
1. Transpose: 2m + m = 10 + 5, so 3m = 15 and m = 5.

Teacher's Note:
1. Collect variable terms on one side.
2. Check: 10 − 5 = 5 = 2 × 5 − 5.

Question 12: What same number should be added to each of the numbers 2, 7, 10 and 25 so that they are in proportion?
(a) 4
(b) 3
(c) 2
(d) 5
Show Answer & Explanation

Answer: (c) 2

Explanation:
1. (2 + x) / (7 + x) = (10 + x) / (25 + x).
2. (2 + x)(25 + x) = (7 + x)(10 + x) gives 50 + 27x + x² = 70 + 17x + x², so 10x = 20 and x = 2.
3. Check: 4 : 9 = 12 : 27.

Teacher's Note:
1. Set the cross products equal; the x² terms cancel.
2. Always check by substituting.

Question 13: A father is 7 times as old as his son. Two years ago the father was 13 times as old as his son. The present age of the son is
(a) 6 years
(b) 5 years
(c) 4 years
(d) 3 years
Show Answer & Explanation

Answer: (c) 4 years

Explanation:
1. Let the son be s and father 7s: 7s − 2 = 13(s − 2), so 6s = 24 and s = 4.
2. Father is 28, check: 26 = 13 × 2.

Teacher's Note:
1. Subtract the same years from both ages.
2. Check with the ages two years ago.

Question 14: Solve: (x + 2)(x + 3) + (x − 3)(x − 2) − 2x(x + 1) = 0.
(a) x = −6
(b) x = −1
(c) x = 2
(d) x = 6
Show Answer & Explanation

Answer: (d) x = 6

Explanation:
1. Expand: x² + 5x + 6 + x² − 5x + 6 − 2x² − 2x = 0.
2. 12 − 2x = 0, so x = 6.

Teacher's Note:
1. Expand every product and watch the cancellations.
2. The x² terms cancel, leaving a linear equation.

Question 15: Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.
(a) 6
(b) 4
(c) 3
(d) 5
Show Answer & Explanation

Answer: (c) 3

Explanation:
1. 5x − 5 = 2x + 4, so 3x = 9 and x = 3.

Teacher's Note:
1. Translate into an equation with the number on both sides.
2. Check: 15 − 5 = 10 = 6 + 4.

Question 16: Sunita is twice as old as Ashima. If six years are subtracted from Ashima's age and four years are added to Sunita's age, Sunita becomes four times Ashima's age. Their present ages are
(a) Sunita 16 years, Ashima 10 years
(b) Sunita 28 years, Ashima 14 years
(c) Sunita 18 years, Ashima 12 years
(d) Sunita 12 years, Ashima 8 years
Show Answer & Explanation

Answer: (b) Sunita 28 years, Ashima 14 years

Explanation:
1. Let Ashima be a, Sunita 2a: 2a + 4 = 4(a − 6), so 2a = 28 and a = 14.
2. Sunita is 28.

Teacher's Note:
1. Apply the given changes to each age before forming the equation.
2. Check: 32 = 4 × 8.

Question 17: 'A' is twice as old as 'B'. Three years ago A's age was three times B's age. The present age of A is
(a) 18 years
(b) 12 years
(c) 6 years
(d) 9 years
Show Answer & Explanation

Answer: (b) 12 years

Explanation:
1. Let B = b and A = 2b: 2b − 3 = 3(b − 3), so b = 6.
2. A = 12 years.

Teacher's Note:
1. Subtract 3 from both ages before applying the condition.
2. Check: 9 = 3 × 3.

Question 18: Find a number whose double is 45 greater than its half.
(a) 25
(b) 30
(c) 33
(d) 19
Show Answer & Explanation

Answer: (b) 30

Explanation:
1. 2x = x/2 + 45, so (3/2)x = 45 and x = 30.

Teacher's Note:
1. Collect the x terms on one side.
2. Check: 60 = 15 + 45.

Question 19: A 100-litre solution of acid and water contains 20 litres of acid. How much water must be added to make the solution 16% acidic?
(a) 30 litres
(b) 25 litres
(c) 33 litres
(d) 19 litres
Show Answer & Explanation

Answer: (b) 25 litres

Explanation:
1. 20 / (100 + w) = 16 / 100, so 100 + w = 125.
2. w = 25 litres.

Teacher's Note:
1. The amount of acid does not change when water is added.
2. Check: 20 / 125 = 16%.

Question 20: A square paper is folded in half breadthwise. The perimeter of the rectangle formed is 12 cm. The area of the square is
(a) 16 cm²
(b) 9 cm²
(c) 36 cm²
(d) 25 cm²
Show Answer & Explanation

Answer: (a) 16 cm²

Explanation:
1. Let the side of the square be s. The rectangle is s by s/2, so perimeter = 3s = 12 and s = 4.
2. Area of the square = 16 cm².

Teacher's Note:
1. Folding in half halves one side only.
2. Perimeter = 2(s + s/2).

Question 21: A boy's age is one-fourth that of his father. After 24 years the boy will be half the age of his father. Their present ages are
(a) Boy 8 years, father 32 years
(b) Boy 6 years, father 24 years
(c) Boy 10 years, father 40 years
(d) Boy 12 years, father 48 years
Show Answer & Explanation

Answer: (d) Boy 12 years, father 48 years

Explanation:
1. Let the boy be b and father 4b: b + 24 = (4b + 24) / 2, so 2b + 48 = 4b + 24 and b = 12.
2. Father = 48.

Teacher's Note:
1. Add 24 to both ages.
2. Check: 36 = half of 72.

Question 22: The sides of a triangle taken in order are each 3 cm longer than the preceding side. If the perimeter is 81 cm, the sides are
(a) 26 cm, 27 cm, 28 cm
(b) 24 cm, 27 cm, 30 cm
(c) 20 cm, 27 cm, 34 cm
(d) 25 cm, 28 cm, 31 cm
Show Answer & Explanation

Answer: (b) 24 cm, 27 cm, 30 cm

Explanation:
1. Sides: x, x + 3, x + 6, so 3x + 9 = 81 and x = 24.

Teacher's Note:
1. Take the shortest side as x.
2. Check: 24 + 27 + 30 = 81.

Question 23: The age of a mother is 25 years more than that of her daughter. Five years hence the mother's age will be twice the daughter's age. Their present ages are
(a) Daughter 10 years, mother 35 years
(b) Daughter 25 years, mother 50 years
(c) Daughter 15 years, mother 40 years
(d) Daughter 20 years, mother 45 years
Show Answer & Explanation

Answer: (d) Daughter 20 years, mother 45 years

Explanation:
1. Let the daughter be d: d + 30 = 2(d + 5), so d = 20.
2. Mother = 45.

Teacher's Note:
1. Add 5 to both ages.
2. Check: 50 = 2 × 25.

Question 24: One number is 5 more than another. Six times the smaller number equals five times the larger. The numbers are
(a) 20 and 25
(b) 25 and 30
(c) 24 and 29
(d) 30 and 35
Show Answer & Explanation

Answer: (b) 25 and 30

Explanation:
1. Let the smaller be x: 6x = 5(x + 5), so x = 25.
2. The numbers are 25 and 30.

Teacher's Note:
1. Larger number = x + 5.
2. Check: 150 = 5 × 30.

Question 25: A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed. The number is
(a) 26
(b) 35
(c) 17
(d) 44
Show Answer & Explanation

Answer: (b) 35

Explanation:
1. Let digits be a and b: a + b = 8 and 10a + b + 18 = 10b + a, so b − a = 2.
2. b = 5 and a = 3, giving 35 (35 + 18 = 53).

Teacher's Note:
1. Reversal adds 9 × (difference of digits).
2. 18 / 9 = 2.

Free study material for Mathematics

Download Chapter MCQs: Class 8 Mathematics Chapter 02 Linear Equations in One Variable

About Chapter 02 Linear Equations in One Variable MCQs for Class 8 Mathematics

Review structured objective questions for Class 8 Mathematics Chapter 02 Linear Equations in One Variable. Built according to official CBSE guidelines, these MCQ sets support daily revision and core concept reinforcement.

How to Verify Your MCQ Answers

Cross-reference your completed choices with comprehensive NCERT solutions for Class 8 Mathematics to ensure absolute clarity across all sub-topics in this chapter.

Enhance Speed with Online MCQ Tests

Explore our broader library of printable assignments, chapter notes, and mock tests designed to support continuous revision and secure higher marks in CBSE assessments.

FAQs

Where can I access latest CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 36?

You can get most exhaustive CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 36 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 One Variable MCQs Set 36 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

How do practicing Mathematics MCQs help in scoring full marks in Class 8 exams?

By solving our CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 36, Class 8 students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 36?

Yes, Mathematics MCQs for Class 8 have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CBSE exams.

Can I practice these Mathematics Class 8 MCQs online?

Yes, you can also access online interactive tests for CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 36 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.