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1. Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages is 3 : 5 ?

A. 10 years

B. 20 years

C. 37 years

D. 5 years

Solution:

\begin{aligned} Harsha  =  40 \\ Ritu  =  60 \\ \frac{Harsha}{Ritu} = \frac{40}{60} \end{aligned}

∴ Let x years ago their ages ratio was 3 : 5

\begin{aligned} \Rightarrow \frac{40 - x}{60 - x} = \frac{3}{5} \\ \Rightarrow 200 - 5 x = 180 - 3 x \\ \Rightarrow 2 x = 20 \\ \Rightarrow x = 10 \end{aligned}

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