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1. The ages of Samina and Suhana are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?

A. 6 years

B. 8 years

C. 10 years

D. 12 years

Solution:

Let Samina's age be 7x years.
Then, Suhana's age = 3x years

\begin{aligned} ∴ \frac{7 x + 6}{3 x + 6} = \frac{5}{3} \\ \Rightarrow 3 (7 x + 6) = 5 (3 x + 6) \\ \Rightarrow 21 x + 18 = 15 x + 30 \\ \Rightarrow 6 x + 12 \\ \Rightarrow x = 2 \end{aligned}

Difference in their ages = (7x - 3x) years
= 4x years
= (4 × 2) years
= 8 years

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