Question

Sandeep has Rs 50 more than Gayatri. When each of them is given Rs 15, the ratio of the money they have becomes 3 : 1. How much money did Gayatri have to begin with?

Answer 1

Let the original money with Sandeep be Rs x
So, the money with Gayatri = Rs (x − 50)
After getting Rs 15 each, ratio of their money becomes 3 : 1.

$$\begin{gathered} \frac{x+15}{x-50+15}=\frac{3}{1} \\ \Rightarrow \frac{x+15}{x-35}=\frac{3}{1} \end{gathered}$$
⇒ x + 15 = 3(x − 35)
⇒ x + 15 = 3x − 105
⇒ 2x = 120
⇒ x = 60
∴ The money with Sandeep = x = Rs 60
and the money with Gayatri = x − 50 = 60-50 = Rs 10