While playing cards, a person loses $75\%$ of his money in the first round, $75\%$ of the remaining in the second round and $75\%$ of the remaining in the third round. If he has Rs $100$ left, how much money did he have initially?

Let the initial amount of money the person had be $X$.In each round, he loses $75\%$ of the money, which means he keeps $25\%$ (or $\frac{1}{4}$) of the money.After the $1^{\text{st}}$ round, money left = $X\times \frac{1}{4}$ After the $2^{\text{nd}}$ round, money left = $X\times \frac{1}{4}\times \frac{1}{4}$ After the $3^{\text{rd}}$ round, money left = $X\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}$ We are given that the remaining money after three rounds is Rs $100$:
$$X\times \frac{1}{64}=100$$
$$X=100\times 64=6400$$
Therefore, he initially had $\text{Rs. }6,400$.