Question

A person spends $\frac{1}{3}$ of his money 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?

• A. Rs. $200$
• B. Rs. $250$
• C. Rs. $300$
• D. Rs. $450$

Answer 1

The correct option is B Rs. $250$

Let the total money with the person be Rs. $x.$
Then, momey spent on cloths $=$ Rs. $\frac{x}{3}$

Remaining money $=$ Rs. $(x-\frac{x}{3})=$ Rs. $\frac{2x}{3}$

$\therefore$ Money spent on food $=$ $\frac{1}{5}\times$ Rs. $\frac{2x}{3}$ =$Rs.\frac{2x}{15}$

Now, remaining money $=$ $\frac{2x}{3}-\frac{2x}{15}=$ Rs. $\frac{8x}{15}$

$\therefore$ Money spent on travel $=$ $\frac{1}{4}\times$ Rs. $\frac{8x}{15}$ $=$ Rs. $\frac{2x}{15}$

Given, $\frac{x}{3}+\frac{2x}{15}+\frac{2x}{15}+100=x$

$\Rightarrow \frac{5x+2x+2x+1500}{15}=x$

$\Rightarrow 9x+1500=15x\Rightarrow 6x=1500$

$\Rightarrow x=\frac{1500}{6}=$ Rs. $250$