CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 45

Download CBSE 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.

Chapter-wise Objective Questions: Chapter 02 Linear Equations in One Variable

View or download the dedicated Chapter 02 Linear Equations in One Variable 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: Solve: \( \frac{3y+4}{2-6y}=\frac{-2}{5} \).
(a) \( -9 \)
(b) \( -8 \)
(c) \( -7 \)
(d) \( 8 \)
Show Answer & Explanation

Answer: (b) \( -8 \)

Explanation:
1. Cross-multiply and collect like terms.
2. 5(3y + 4) = -2(2 - 6y) gives 15y + 20 = -4 + 12y, so y = -8.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 2: Solve: \( \frac{7y+4}{y+2}=\frac{-4}{3} \).
(a) \( \frac{4}{5} \)
(b) \( \frac{1}{5} \)
(c) \( -\frac{9}{5} \)
(d) \( -\frac{4}{5} \)
Show Answer & Explanation

Answer: (d) \( -\frac{4}{5} \)

Explanation:
1. Cross-multiply and collect like terms.
2. 3(7y + 4) = -4(y + 2) gives 25y = -20, so y = -4/5.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 3: Solve: \( 5x - 3 = 3x - 5 \).
(a) \( -2 \)
(b) \( 1 \)
(c) \( -1 \)
(d) \( 0 \)
Show Answer & Explanation

Answer: (c) \( -1 \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( -1 \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 4: Solve: \( 5x + 9 = 5 + 3x \).
(a) \( 0 \)
(b) \( -1 \)
(c) \( 1 \)
(d) \( -2 \)
Show Answer & Explanation

Answer: (d) \( -2 \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( -2 \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 5: Solve: \( 4x + 3 = 6 + 2x \).
(a) \( \frac{3}{2} \)
(b) \( 0 \)
(c) \( 1 \)
(d) \( -1 \)
Show Answer & Explanation

Answer: (a) \( \frac{3}{2} \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( \frac{3}{2} \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 6: Solve: \( 2x - 1 = 14 - x \).
(a) \( 1 \)
(b) \( 5 \)
(c) \( -1 \)
(d) \( 0 \)
Show Answer & Explanation

Answer: (b) \( 5 \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( 5 \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 7: Solve: \( x = \frac{4}{5}(x + 10) \).
(a) \( 0 \)
(b) \( 40 \)
(c) \( 1 \)
(d) \( -1 \)
Show Answer & Explanation

Answer: (b) \( 40 \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( 40 \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 8: Solve: \( \frac{2x}{3} + 1 = \frac{7x}{15} + 3 \).
(a) \( -1 \)
(b) \( 1 \)
(c) \( 0 \)
(d) \( 10 \)
Show Answer & Explanation

Answer: (d) \( 10 \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( 10 \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 9: Solve: \( 2x + \frac{5}{3} = \frac{26}{3} - x \).
(a) \( 0 \)
(b) \( -1 \)
(c) \( 1 \)
(d) \( \frac{7}{3} \)
Show Answer & Explanation

Answer: (d) \( \frac{7}{3} \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( \frac{7}{3} \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 10: Solve: \( 3x = 5x - \frac{8}{5} \).
(a) \( 0 \)
(b) \( \frac{4}{5} \)
(c) \( 1 \)
(d) \( -1 \)
Show Answer & Explanation

Answer: (b) \( \frac{4}{5} \)

Explanation:
1. Collect variable terms on one side and constants on the other.
2. Solving gives x = \( \frac{4}{5} \).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 11: If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. The number is:
(a) \( \frac{3}{4} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{5}{4} \)
(d) \( \frac{1}{4} \)
Show Answer & Explanation

Answer: (a) \( \frac{3}{4} \)

Explanation:
1. (x - 1/2) x 1/2 = 1/8 gives x - 1/2 = 1/4.
2. x = 3/4.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 12: The base of an isosceles triangle is 4/3 cm and its perimeter is 62/15 cm. The length of either of the equal sides (in cm) is:
(a) \( \frac{14}{15} \)
(b) \( \frac{7}{3} \)
(c) \( \frac{21}{5} \)
(d) \( \frac{7}{5} \)
Show Answer & Explanation

Answer: (d) \( \frac{7}{5} \)

Explanation:
1. 2s = 62/15 - 4/3 = 62/15 - 20/15 = 42/15.
2. s = 21/15 = 7/5 cm.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 13: The sum of two numbers is 95. If one exceeds the other by 15, the larger number is:
(a) 40
(b) 50
(c) 45
(d) 55
Show Answer & Explanation

Answer: (d) 55

Explanation:
1. x + (x + 15) = 95 gives x = 40.
2. Numbers are 40 and 55.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 14: Two numbers are in the ratio 5 : 3. If they differ by 18, the larger number is:
(a) 45
(b) 27
(c) 30
(d) 54
Show Answer & Explanation

Answer: (a) 45

Explanation:
1. 5x - 3x = 18 gives x = 9.
2. Numbers are 45 and 27.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 15: Three consecutive integers add up to 51. The largest is:
(a) 19
(b) 16
(c) 17
(d) 18
Show Answer & Explanation

Answer: (d) 18

Explanation:
1. x + (x + 1) + (x + 2) = 51 gives x = 16.
2. The integers are 16, 17, 18.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 16: Three consecutive integers are such that when taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. The smallest integer is:
(a) 8
(b) 7
(c) 6
(d) 9
Show Answer & Explanation

Answer: (b) 7

Explanation:
1. 2x + 3(x + 1) + 4(x + 2) = 74 gives 9x + 11 = 74.
2. x = 7, so the integers are 7, 8, 9.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 17: The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later the sum of their ages will be 56 years. Haroon's present age is:
(a) 28
(b) 24
(c) 20
(d) 32
Show Answer & Explanation

Answer: (a) 28

Explanation:
1. 5x + 4 + 7x + 4 = 56 gives x = 4.
2. Rahul 20, Haroon 28.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 18: The numbers of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. The total class strength is:
(a) 40
(b) 36
(c) 52
(d) 48
Show Answer & Explanation

Answer: (d) 48

Explanation:
1. 7x - 5x = 8, so x = 4: 28 boys and 20 girls.
2. Total = 48.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 19: Baichung's father is 26 years younger than Baichung's grandfather and 29 years older than Baichung. The sum of the ages of all three is 135 years. Baichung's grandfather's age (in years) is:
(a) 75
(b) 17
(c) 72
(d) 46
Show Answer & Explanation

Answer: (c) 72

Explanation:
1. Baichung b, father b + 29, grandfather b + 55: 3b + 84 = 135, so b = 17.
2. Grandfather = 72.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 20: Fifteen years from now Ravi's age will be four times his present age. Ravi's present age (in years) is:
(a) 5
(b) 3
(c) 15
(d) 10
Show Answer & Explanation

Answer: (a) 5

Explanation:
1. x + 15 = 4x gives x = 5.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 21: Lakshmi has notes of Rs. 100, Rs. 50 and Rs. 10 in the ratio 2 : 3 : 5. Her total cash is Rs. 4,00,000. The number of Rs. 50 notes she has is:
(a) 5000
(b) 1500
(c) 2000
(d) 3000
Show Answer & Explanation

Answer: (d) 3000

Explanation:
1. Let the numbers be 2k, 3k and 5k: 200k + 150k + 50k = 400000, so k = 1000.
2. Rs. 50 notes = 3000 (Rs. 100: 2000 and Rs. 10: 5000).

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Question 22: In an essay competition a winner gets Rs. 100 and a participant who does not win gets Rs. 25. The total prize money is Rs. 3,000 and there are 63 participants. The number of winners is:
(a) 18
(b) 20
(c) 19
(d) 21
Show Answer & Explanation

Answer: (c) 19

Explanation:
1. 100w + 25(63 - w) = 3000 gives 75w = 1425.
2. w = 19.

Teacher's Note:
1. Define the unknown, translate each sentence into an equation and solve it step by step.
2. Always substitute the answer back into the original statement to check it.

Free study material for Mathematics

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

Download Multiple Choice Questions: Chapter 02 Linear Equations in One Variable (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.

Concept Clarification for Chapter 02 Linear Equations in One Variable

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

Additional Study Resources for Class 8 Mathematics

Follow up your worksheet practice by attempting the interactive online Mathematics MCQ test for this chapter to evaluate your execution speed. All platform resources are free to access.

FAQs

Where can I access latest CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 45?

You can get most exhaustive CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 45 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 45 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 45, 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 45?

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 45 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.