Question

A man loses $20\%$ of his money. After spending $25\%$ of the remainder, he has Rs 480 left. How much money did he originally have?

Answer 1

Let the money that the man has be $x.$

Money lost $=20\%$ of original money $=20\%$ of $x=0.2\times x$

Money he has after losing $=$ Original money $-$ money lost

$=x-0.2x=0.8x$

After that, Money spent $=25\%$ of money after losing

$=0.25\times 0.8x$

$=0.2x$

Money Left $=$ Money after losing $-$ Money spent

$=0.8x-0.2x=0.6x$

But Money left is given as $Rs.480.$

$\therefore 0.6x=480$

$\Rightarrow x=\frac{480}{0.6}$

$\therefore x=800$

so, he originally had $Rs.800$.

OR

Since he loses $20\%$ of the money, he is left with $80\%$ of the money, which can be written as $\left(\frac{80}{100}\right)\times x=0.8x$

Now, he spends $25\%$ of this money. So after spending, he is left with $75\%$ of that money.

That would be $\left(\frac{75}{100}\right)\times \left(0.8x\right)=0.6x$

We are given that

$0.6x=480$

On solving, we get x = Rs. 800