Question

A person spends $\frac{1}{3}$ of the money with him on clothes, $\frac{1}{5}$ of the remaining on food and $\frac{1}{4}$ of the remaining on travel. Now, he is left with Rs 100. How much did he have with him in the beginning?

Answer 1

Let the person have $x$ as the total amount in the beginning then

According to the given condition-

Total expenses on cloths $=\frac{1}{3}\times x\Rightarrow \frac{x}{3}$
Remaining balance $=x-\frac{x}{3}\Rightarrow \frac{2x}{3}$
Total expenses on food $=\frac{1}{5}\times \frac{2x}{3}\Rightarrow \frac{2x}{15}$
Remaining balance $=\frac{2x}{3}-\frac{2x}{15}\Rightarrow \frac{8x}{15}$
Total expenses on travel $=\frac{1}{4}\times \frac{8x}{15}\Rightarrow \frac{2x}{15}$
Now, he is left with $Rs.100$
$\therefore \frac{2x}{5}=100$
$2x=500$
$x=Rs.250.$

Hence, the person had $Rs.250$ oin the beginning.