CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 41

Multiple Choice Questions (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.

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

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: A number is as much greater than 36 as 86 is greater than the number. The number is:
(a) 60
(b) 63
(c) 62
(d) 61
Show Answer & Explanation

Answer: (d) 61

Explanation:
1. Let the number be x: x - 36 = 86 - x.
2. 2x = 122, so x = 61.

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 2: When 15 is subtracted from 7 times a number, the result is 10 more than twice the number. The number is:
(a) 6
(b) 5
(c) 4
(d) 7
Show Answer & Explanation

Answer: (b) 5

Explanation:
1. 7x - 15 = 2x + 10.
2. 5x = 25, so 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 3: The sum of two numbers is 184. If one-third of one exceeds one-seventh of the other by 8, the smaller number is:
(a) 92
(b) 56
(c) 112
(d) 72
Show Answer & Explanation

Answer: (d) 72

Explanation:
1. Let the numbers be x and y: x + y = 184 and x/3 - y/7 = 8, i.e. 7x - 3y = 168.
2. Substituting y = 184 - x: 10x = 720, x = 72 and y = 112.
3. The smaller number is 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 4: The difference of two numbers is 11 and one-fifth of their sum is 9. The larger number is:
(a) 28
(b) 17
(c) 26
(d) 34
Show Answer & Explanation

Answer: (a) 28

Explanation:
1. x - y = 11 and (x + y)/5 = 9 gives x + y = 45.
2. Adding: 2x = 56, so x = 28 and y = 17.

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: The sum of two numbers is 42 and their product is 437. The difference between the numbers is:
(a) 2
(b) 6
(c) 8
(d) 4
Show Answer & Explanation

Answer: (d) 4

Explanation:
1. The numbers are roots of t^2 - 42t + 437 = 0, i.e. 19 and 23.
2. Difference = 4.

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: The sum of two numbers is 15 and the sum of their squares is 113. The larger number is:
(a) 9
(b) 7
(c) 10
(d) 8
Show Answer & Explanation

Answer: (d) 8

Explanation:
1. xy = ((x + y)^2 - (x^2 + y^2))/2 = (225 - 113)/2 = 56.
2. The numbers satisfy t^2 - 15t + 56 = 0: 7 and 8.

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: The average of four consecutive even numbers is 27. The largest of these numbers is:
(a) 28
(b) 27
(c) 32
(d) 30
Show Answer & Explanation

Answer: (d) 30

Explanation:
1. Let the numbers be x, x+2, x+4, x+6: 4x + 12 = 108, so x = 24.
2. The numbers are 24, 26, 28, 30; the largest is 30.

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: Of two numbers, 4 times the smaller is 5 less than 3 times the larger. Also the sum of the numbers is larger than 5 times their difference by 22. The larger number is:
(a) 59
(b) 49
(c) 43
(d) 53
Show Answer & Explanation

Answer: (a) 59

Explanation:
1. 4s = 3l - 5 and s + l = 5(l - s) + 22, i.e. 3s - 2l = 11.
2. Solving: s = 43 and l = 59.

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: The ratio between a two-digit number and the sum of its digits is 4 : 1. If the digit in the unit's place is 3 more than the digit in the ten's place, the number is:
(a) 47
(b) 36
(c) 14
(d) 25
Show Answer & Explanation

Answer: (b) 36

Explanation:
1. Let the digits be a and a + 3: 10a + (a + 3) = 4(2a + 3).
2. 3a = 9, so a = 3 and the number is 36.

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: A two-digit number has digit sum 9. If 63 is subtracted from it, its digits get interchanged. The number is:
(a) 81
(b) 72
(c) 63
(d) 90
Show Answer & Explanation

Answer: (a) 81

Explanation:
1. Let the number be 10a + b with a + b = 9.
2. 10a + b - 63 = 10b + a gives a - b = 7, so a = 8 and b = 1; the number is 81.

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: A fraction becomes 2/3 when 1 is added to both numerator and denominator, and 1/2 when 1 is subtracted from both. The fraction is:
(a) \( \frac{3}{5} \)
(b) \( \frac{2}{3} \)
(c) \( \frac{3}{7} \)
(d) \( \frac{5}{3} \)
Show Answer & Explanation

Answer: (a) \( \frac{3}{5} \)

Explanation:
1. (x + 1)/(y + 1) = 2/3 gives 3x + 3 = 2y + 2, and (x - 1)/(y - 1) = 1/2 gives y = 2x - 1.
2. Then 3x + 3 = 2(2x - 1) + 2 = 4x, so x = 3 and y = 5; the fraction is 3/5.

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 12: If three numbers are added in pairs, the sums are 10, 19 and 21. The largest number is:
(a) 15
(b) 10
(c) 19
(d) 6
Show Answer & Explanation

Answer: (a) 15

Explanation:
1. Adding the three sums gives 2(a + b + c) = 50, so a + b + c = 25.
2. The numbers are 25 - 10 = 15, 25 - 19 = 6 and 25 - 21 = 4.

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 13: Rajeev's age after 15 years will be 5 times his age 5 years back. His present age (in years) is:
(a) 12
(b) 10
(c) 8
(d) 15
Show Answer & Explanation

Answer: (b) 10

Explanation:
1. x + 15 = 5(x - 5) gives 4x = 40.
2. 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 14: The ages of two persons differ by 16 years. If 6 years ago the elder was 3 times as old as the younger, the present age of the elder is:
(a) 14
(b) 30
(c) 28
(d) 32
Show Answer & Explanation

Answer: (b) 30

Explanation:
1. Let the younger be y: y + 10 = 3(y - 6), so y = 14.
2. Elder = 14 + 16 = 30.

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: The product of the ages of Ankit and Nikita is 240. If twice Nikita's age is 4 more than Ankit's age, Nikita's age is:
(a) 20
(b) 15
(c) 10
(d) 12
Show Answer & Explanation

Answer: (d) 12

Explanation:
1. Let Nikita be n: Ankit = 2n - 4, so n(2n - 4) = 240, i.e. n^2 - 2n - 120 = 0.
2. (n - 12)(n + 10) = 0, so n = 12 (Ankit = 20).

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: A father's present age is 3 years more than three times the age of his son. Three years hence, the father's age will be 10 years more than twice the age of the son. The father's present age is:
(a) 33
(b) 30
(c) 36
(d) 43
Show Answer & Explanation

Answer: (a) 33

Explanation:
1. F = 3S + 3 and F + 3 = 2(S + 3) + 10.
2. 3S + 6 = 2S + 16, so S = 10 and F = 33.

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: One year ago the ratio of Gaurav's and Sachin's ages was 6 : 7. Four years hence it will be 7 : 8. Sachin's present age is:
(a) 35
(b) 36
(c) 31
(d) 40
Show Answer & Explanation

Answer: (b) 36

Explanation:
1. (G - 1)/(S - 1) = 6/7 gives 7G = 6S + 1; (G + 4)/(S + 4) = 7/8 gives 8G = 7S - 4.
2. Eliminating G: 8(6S + 1) = 7(7S - 4), so S = 36 (G = 31).

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: Abhay's age after six years will be three-seventh of his father's present age. The father's present age is 4 more than three times Abhay's present age. The father's present age is:
(a) 46
(b) 45
(c) 49
(d) 52
Show Answer & Explanation

Answer: (c) 49

Explanation:
1. A + 6 = 3F/7 and F = 3A + 4.
2. 7A + 42 = 9A + 12, so A = 15 and F = 49.

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: The ages of Hari and Harry are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. Harry's present age is:
(a) 20
(b) 32
(c) 24
(d) 28
Show Answer & Explanation

Answer: (d) 28

Explanation:
1. Let the ages be 5x and 7x: 4(5x + 4) = 3(7x + 4).
2. x = 4, so Harry is 28 and Hari is 20.

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: The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. The rational number is:
(a) \( \frac{11}{19} \)
(b) \( \frac{21}{13} \)
(c) \( \frac{17}{25} \)
(d) \( \frac{13}{21} \)
Show Answer & Explanation

Answer: (d) \( \frac{13}{21} \)

Explanation:
1. Let the number be x/(x + 8): (x + 17)/(x + 7) = 3/2.
2. 2x + 34 = 3x + 21 gives x = 13, so the number is 13/21.

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 21: Solve: \( \frac{8x-3}{3x}=2 \).
(a) \( \frac{5}{2} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{3}{2} \)
(d) \( -\frac{3}{2} \)
Show Answer & Explanation

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

Explanation:
1. Cross-multiply and collect like terms.
2. 8x - 3 = 6x, so x = 3/2.

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 22: Solve: \( \frac{9x}{7-6x}=15 \).
(a) \( \frac{35}{33} \)
(b) \( \frac{68}{33} \)
(c) \( -\frac{35}{33} \)
(d) \( \frac{2}{33} \)
Show Answer & Explanation

Answer: (a) \( \frac{35}{33} \)

Explanation:
1. Cross-multiply and collect like terms.
2. 9x = 105 - 90x, so 99x = 105 and x = 35/33.

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 23: Solve: \( \frac{z}{z+15}=\frac{4}{9} \).
(a) \( 13 \)
(b) \( 11 \)
(c) \( -12 \)
(d) \( 12 \)
Show Answer & Explanation

Answer: (d) \( 12 \)

Explanation:
1. Cross-multiply and collect like terms.
2. 9z = 4z + 60, so z = 12.

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.

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

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