CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 29

Answer: (c) 7

Explanation:
1. x − 4 = 21/x, so x² − 4x − 21 = 0.
2. (x − 7)(x + 3) = 0, and the positive number is 7.

Teacher's Note:
1. Translate the words into an equation, using x for the unknown number.
2. Always substitute the answer back into the statement to check it.

Answer: (a) \( \sqrt2 \)

Explanation:
1. x + 1/x = 3(x − 1/x), so 4/x = 2x.
2. x² = 2, so x = \( \sqrt2 \).

Teacher's Note:
1. Write the condition as a single linear equation and solve step by step.
2. Check your result against the original wording, not only against the equation.

Answer: (c) \( \frac{290}{289} \)

Explanation:
1. 17 is prime, so the numbers are 1 and 17.
2. \( \frac1{1^2}+\frac1{17^2}=1+\frac1{289}=\frac{290}{289} \)

Teacher's Note:
1. Translate the words into an equation, using x for the unknown number.
2. Always substitute the answer back into the statement to check it.

Answer: (b) \( 3\frac12 \)

Explanation:
1. Let the number be x: \( \frac{(x+\frac52)\times\frac92+3}{\frac65}=25 \).
2. The numerator must be 25 × 6/5 = 30, so (x + 5/2) × 9/2 = 27 and x + 5/2 = 6.
3. x = 3.5, that is \( 3\frac12 \).

Teacher's Note:
1. Write the condition as a single linear equation and solve step by step.
2. Check your result against the original wording, not only against the equation.

Answer: (a) 30

Explanation:
1. Total = 3 × 25 = 75 = 15x, so x = 5.
2. Largest = 6 × 5 = 30.

Teacher's Note:
1. Write the quantities as multiples of a common unknown, such as 4x and 7x.
2. Use the extra condition to form one equation in x.

Answer: (c) 18

Explanation:
1. The numbers are 3x, 4x, 6x: 72x³ = 1944, so x³ = 27 and x = 3.
2. Largest = 6 × 3 = 18.

Teacher's Note:
1. Introduce a common factor x for the ratio and form an equation from the given condition.
2. Then find the required quantity, not only x.

Answer: (a) 6, 8

Explanation:
1. Let the numbers be 3x and 4x: (4x)² = 8(3x)² − 224.
2. 16x² = 72x² − 224, so 56x² = 224 and x = 2.
3. The numbers are 6 and 8.

Teacher's Note:
1. Write the quantities as multiples of a common unknown, such as 4x and 7x.
2. Use the extra condition to form one equation in x.

Answer: (c) 56

Explanation:
1. Let the numbers be 4x and 7x: 5(4x + 4) = 3(7x + 4).
2. 20x + 20 = 21x + 12, so x = 8.
3. Larger number = 7 × 8 = 56.

Teacher's Note:
1. Introduce a common factor x for the ratio and form an equation from the given condition.
2. Then find the required quantity, not only x.

Answer: (c) 72

Explanation:
1. Let the second number be y: first = 2y, third = 2y/3.
2. 2y + y + 2y/3 = 264, so 11y/3 = 264 and y = 72.

Teacher's Note:
1. Translate the words into an equation, using x for the unknown number.
2. Always substitute the answer back into the statement to check it.

Answer: (b) 12

Explanation:
1. Let the numbers be a and b: a + b = 22 and 5a = 6b, so a = 6b/5.
2. 6b/5 + b = 22 gives b = 10 and a = 12.

Teacher's Note:
1. Write the condition as a single linear equation and solve step by step.
2. Check your result against the original wording, not only against the equation.

Answer: (b) 40

Explanation:
1. Let the numbers be a and b: a/5 = 5b/8, so a = 25b/8.
2. 35 + a = 4b gives 35 + 25b/8 = 4b, so 7b/8 = 35 and b = 40.

Teacher's Note:
1. Translate the words into an equation, using x for the unknown number.
2. Always substitute the answer back into the statement to check it.

Answer: (b) 114

Explanation:
1. The numbers are (25 + 13)/2 = 19 and (25 − 13)/2 = 6.
2. Product = 19 × 6 = 114.

Teacher's Note:
1. Write the condition as a single linear equation and solve step by step.
2. Check your result against the original wording, not only against the equation.

Answer: (a) 9

Explanation:
1. Smaller number = (33 − 15)/2 = 9.

Teacher's Note:
1. Translate the words into an equation, using x for the unknown number.
2. Always substitute the answer back into the statement to check it.

Answer: (a) 11 : 9

Explanation:
1. The numbers are 22 and 18.
2. Ratio = 22 : 18 = 11 : 9.

Teacher's Note:
1. Write the condition as a single linear equation and solve step by step.
2. Check your result against the original wording, not only against the equation.

Answer: (a) 12

Explanation:
1. Let the numbers be x and 28 − x: x(28 − x) = 192, so x² − 28x + 192 = 0.
2. (x − 12)(x − 16) = 0, so the smaller number is 12.

Teacher's Note:
1. Translate the words into an equation, using x for the unknown number.
2. Always substitute the answer back into the statement to check it.

Answer: (d) None of these

Explanation:
1. Let the ages be 7x and 9x: 9x − 7x = 4, so x = 2.
2. Sachin's age = 14 years, which is not among options (a), (b), (c).

Teacher's Note:
1. Express every age at the time mentioned in the question and equate the given ratio.
2. Check the answer by counting the years forward and backward.

Answer: (d) None of these

Explanation:
1. Ages are 6x and 7x: 7x − 6x = 4, so x = 4: P = 24, Q = 28.
2. After 4 years: 28 : 32 = 7 : 8, which is not among options (a), (b), (c).

Teacher's Note:
1. Present ages are written as ratio multiples; ages in the past or future add or subtract the same number of years.
2. The difference between two ages never changes with time.

Answer: (a) 48 years

Explanation:
1. Ages are 5x and 7x: 7x − (5x + 6) = 2, so x = 4.
2. Total = 12x = 48 years.

Teacher's Note:
1. Express every age at the time mentioned in the question and equate the given ratio.
2. Check the answer by counting the years forward and backward.

Answer: (b) 15 years

Explanation:
1. Arun's present age = 26 − 6 = 20, so 4x = 20 and x = 5.
2. Deepak's present age = 3 × 5 = 15 years.

Teacher's Note:
1. Present ages are written as ratio multiples; ages in the past or future add or subtract the same number of years.
2. The difference between two ages never changes with time.