A boy spends `1/3` of his money in a shop, then he goes to another shop and spends `1/2` of that was left. He is left with Rs. 15. Find out how much total money did he has?

Answer

To solve the problem step by step, we can follow these calculations:

1. **Let the total amount of money the boy initially had be \( x \)**.
\[ \text{Total money} = x \]

**Hint**: Define a variable for the total amount of money to make calculations easier.

2. **The boy spends \( \frac{1}{3} \) of his money in the first shop**. Therefore, the amount spent in the first shop is:
\[ \text{Amount spent in first shop} = \frac{1}{3}x \]

**Hint**: Calculate the fraction of money spent to understand how much is left.

3. **Calculate the remaining money after the first shop**:
\[ \text{Remaining money} = x - \frac{1}{3}x = \frac{2}{3}x \]

**Hint**: Subtract the amount spent from the total to find out how much is left.

4. **The boy then spends \( \frac{1}{2} \) of the remaining money in the second shop**. The amount spent in the second shop is:
\[ \text{Amount spent in second shop} = \frac{1}{2} \left(\frac{2}{3}x\right) = \frac{1}{3}x \]

**Hint**: Use the remaining amount to calculate the next fraction spent.

5. **Calculate the remaining money after the second shop**:
\[ \text{Remaining money} = \frac{2}{3}x - \frac{1}{3}x = \frac{1}{3}x \]

**Hint**: Again, subtract the amount spent from the remaining money to find out how much is left.

6. **According to the problem, the boy is left with Rs. 15**:
\[ \frac{1}{3}x = 15 \]

**Hint**: Set up an equation based on the information given in the problem.

7. **Solve for \( x \)**:
\[ x = 15 \times 3 = 45 \]

**Hint**: Multiply both sides of the equation by 3 to isolate \( x \).

8. **Conclusion**: The total amount of money the boy initially had is Rs. 45.

**Final Answer**: The boy had Rs. 45.