Problems on Ages — “Surabhi : Neerja = 6 : 7 at present. After 6 years the ratio becomes 15 : 17. Find Neerja’s present age.”
-
A24 years
-
B26 years
-
C28 years
-
D32 years
-
E30 years
Answer
Correct Answer: 28 years
Explanation
Introduction / Context:When a present-time ratio and a future ratio are given, express present ages using a common multiplier, then apply the future condition to determine that multiplier.
Given Data / Assumptions:
- Now: Surabhi : Neerja = 6 : 7 ⇒ S = 6x, N = 7x.
- After 6 years: (S + 6) : (N + 6) = 15 : 17.
Concept / Approach:Set up a proportion with the unknown x and solve by cross-multiplication. Integers are expected for typical age problems.
Step-by-Step Solution:
(6x + 6)/(7x + 6) = 15/17.17(6x + 6) = 15(7x + 6) ⇒ 102x + 102 = 105x + 90.Rearrange: 12 = 3x ⇒ x = 4.Neerja N = 7x = 28 years.Verification / Alternative check:Now (24, 28) → after 6 years (30, 34) = 15:17 ✓.
Why Other Options Are Wrong:24/26/30/32 years break the 15:17 future ratio when paired with S = 6x.
Common Pitfalls:Using the same multiplier for future ages instead of adding years; or incorrectly simplifying the ratio before substitution.
Final Answer:28 years