Question

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

Answer 1

Assume that initially he had Rs. X

He spent $\frac{1}{3}$ for cloths $=\frac{1}{3}\times X$

Remaining money $=\frac{2}{3}\times X$

He spent $\frac{1}{5}$ of remaining money for food $=\frac{1}{5}\times \frac{2x}{3}=\frac{2x}{15}$

Remaining money $=\frac{2x}{3}-\frac{2x}{15}=\frac{8x}{15}$

Again, he spent $\frac{1}{4}$ of remaining money for travel $=\frac{1}{4}\times \frac{8x}{15}=\frac{2x}{15}$

Remaining money $=\frac{8x}{15}-\frac{2x}{15}=\frac{6x}{15}$

But after spending for travel he is left with Rs. 100. So,

$\frac{6x}{15}=100$

$x=Rs.250$