Present ages are in the ratio 2 : 5 (A : B). After 8 years, their ages will be in the ratio 1 : 2. What is the difference between their present ages?

Difficulty: Medium

20 years
24 years
26 years
29 years
None of these

Correct Answer: 24 years

Explanation:

Introduction / Context:
Ratios of ages at two different times allow us to parameterize present ages and apply a future ratio condition. We then compute the numeric ages and their difference.

Given Data / Assumptions:

Now: A : B = 2 : 5 ⇒ A = 2x, B = 5x.
After 8 years: (A + 8) : (B + 8) = 1 : 2.
Find the present-age difference B − A.

Concept / Approach:
Substitute A = 2x and B = 5x into the future ratio and solve for x. The present difference is (5x − 2x).

Step-by-Step Solution:

(A + 8)/(B + 8) = 1/2 ⇒ 2(A + 8) = (B + 8).2(2x + 8) = 5x + 8 ⇒ 4x + 16 = 5x + 8 ⇒ x = 8.Present ages: A = 16, B = 40. Difference = 24 years.

Verification / Alternative check:

After 8 years: A = 24, B = 48 ⇒ 24 : 48 = 1 : 2 ✔.

Why Other Options Are Wrong:

20, 26, 29 are inconsistent with the future ratio.

Common Pitfalls:

Forgetting to add 8 to both ages when forming the future ratio.Assuming the difference remains proportional (it does not; it is absolute).

Present ages are in the ratio 2 : 5 (A : B). After 8 years, their ages will be in the ratio 1 : 2. What is the difference between their present ages?

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