Age ratio now, ratio after 10 years: The present ages of Vikas and Vishal are in the ratio 15:8. After 10 years, their ages will be in the ratio 5:3. Find their current ages in years.

Introduction / Context:Age-ratio problems often require setting up variables from the initial ratio and then applying a time shift to match a future ratio. Solving the resulting equation yields the scale factor and thus the present ages.

Given Data / Assumptions:

• Now: Vikas : Vishal = 15 : 8 → ages = 15x and 8x
• After 10 years: (15x + 10) : (8x + 10) = 5 : 3

Concept / Approach:Cross-multiply the future ratio to solve for x. Then compute actual ages by multiplying the ratio terms by x.

Step-by-Step Solution:3(15x + 10) = 5(8x + 10)45x + 30 = 40x + 50 → 5x = 20 → x = 4Ages now: 15x = 60 years; 8x = 32 years

Verification / Alternative check:After 10 years: 70 and 42, ratio 70:42 = 5:3, so the condition holds.

Why Other Options Are Wrong:Reversed orders or unreduced ratios do not satisfy the future ratio condition when checked.

Common Pitfalls:Forgetting to add 10 to both ages or cross-multiplying incorrectly in the ratio equation.

Final Answer:60 years, 32 years