Question

The difference between the present ages of Trisha and Shalini is 14 years. Seven years ago, the ratio of their ages was 5:7 respectively. What is Shalini’s present age?

• A. 49 years
• B. 56 years
• C. 63 years
• D. 40 years

Hint:

Translate age ratio and difference problems into algebraic equations, then solve stepwise.

Answer 1

The Correct Option is B

Let the present ages of Trisha and Shalini be \(T\) and \(S\) respectively.
Given:
\[ S - T = 14 \] Seven years ago:
\[ \frac{T - 7}{S - 7} = \frac{5}{7} \] Cross multiply:
\[ 7(T - 7) = 5(S - 7) \] \[ 7T - 49 = 5S - 35 \] \[ 7T - 5S = 14 \] Using \(S = T + 14\), substitute:
\[ 7T - 5(T + 14) = 14 \] \[ 7T - 5T - 70 = 14 \] \[ 2T = 84 \] \[ T = 42 \] So, \[ S = T + 14 = 42 + 14 = 56 \] Check the ratio 7 years ago:
\[ \frac{42 - 7}{56 - 7} = \frac{35}{49} = \frac{5}{7} \] Hence, Shalini’s present age is \(\boxed{56}\) years.