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1. The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?

A. 2 Years

B. 4 Years

C. 8 Years

D. 6 Years

Solution:

Let Shakti's age be 8

x

years,
Then Kanti's age = 7

x

years

\begin{aligned} ∴ \frac{8 x + 10}{7 x + 10} = \frac{13}{12} \\ \Rightarrow 12 (8 x + 10) = 13 (7 x + 10) \\ \Rightarrow 96 x + 120 = 91 x + 130 \\ \Rightarrow 5 x = 10 \\ \Rightarrow x = 2 \end{aligned}

Difference between their ages

\begin{aligned} = (8 x - 7 x) \\ = x years \\ =  2 years \end{aligned}

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