Sunitha and Pranitha are 40 years and 60 years old respectively at present. How many years ago was the ratio of their ages exactly 3:5?

Introduction:
This question checks how to handle age ratios in the past. When we go back by t years, both people's ages reduce by the same t. So if Sunitha is 40 and Pranitha is 60 now, then t years ago they were (40 - t) and (60 - t). The ratio condition (40 - t)/(60 - t) = 3/5 gives a single equation in t, which can be solved using cross-multiplication.

Given Data / Assumptions:

• Sunitha's present age = 40 years
• Pranitha's present age = 60 years
• t years ago, ratio was 3 : 5
• So (40 - t)/(60 - t) = 3/5

Concept / Approach:
Use past ages with variable t and solve the ratio equation by cross-multiplying.

Step-by-Step Solution:
t years ago, ages were: 40 - t and 60 - tGiven ratio: (40 - t)/(60 - t) = 3/5Cross-multiply: 5(40 - t) = 3(60 - t)200 - 5t = 180 - 3t200 - 180 = 5t - 3t20 = 2t => t = 10

Verification / Alternative check:
10 years ago: Sunitha was 30 and Pranitha was 50. Ratio 30:50 simplifies to 3:5, which matches the condition exactly.

Why Other Options Are Wrong:
15 years: would give ages 25 and 45, ratio 25:45 = 5:9, not 3:5.18 years: gives 22 and 42, ratio 11:21, not 3:5.24 years: gives 16 and 36, ratio 4:9, not 3:5.12 years: gives 28 and 48, ratio 7:12, not 3:5.

Common Pitfalls:
Subtracting different values from each age instead of the same t.Using 40/60 = 2/3 and confusing it with the required 3/5 ratio.Not simplifying the ratio after computing past ages.

Final Answer:
10 years