A person loses `75%` of his money in the first bat, `75%` of remaining in the second and `75%` of remaining in the third bet and returns home with `Rs.2` only. His initial money was ?

Options

A. Rs. `128`
B. Rs. `132`
C. Rs. `124`
D. Rs. `125`

Answer

To find the initial amount of money the person had, we can work backwards from the final amount he has after all the bets.

Let's denote the initial amount of money as \( x \).

1. **After the first bet:**
- The person loses 75% of his money.
- Remaining money after the first bet = \( x - 0.75x = 0.25x \).

2. **After the second bet:**
- The person loses 75% of the remaining money.
- Remaining money after the second bet = \( 0.25x - 0.75(0.25x) = 0.25x - 0.1875x = 0.0625x \).

3. **After the third bet:**
- The person loses 75% of the remaining money again.
- Remaining money after the third bet = \( 0.0625x - 0.75(0.0625x) = 0.0625x - 0.046875x = 0.015625x \).

4. **Final amount:**
- We know that after all three bets, the person has Rs. 2.
- Therefore, we can set up the equation:
\[ 0.015625x = 2 \]

5. **Solving for \( x \):**
- To find \( x \), divide both sides by 0.015625:
\[ x = \frac{2}{0.015625} \]

6. **Calculating \( x \):**
- Performing the division:
\[ x = 128 \]

Thus, the initial amount of money the person had was **Rs. 128**.