A father gives 1% of his monthly salary to his two sons as pocket money. The elder son gets 80% of the total amount given to the two sons and he spends 80% of his share. If he saves 20 every month, then the monthly salary of the father is

Options

A. 10000
B. 11500
C. 12500
D. 12000

Answer

To find the father's monthly salary based on the information provided, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Assume the Monthly Salary**:
Let the father's monthly salary be \( x \).

2. **Calculate the Total Pocket Money**:
The father gives 1% of his monthly salary as pocket money to his two sons.
\[ \text{Total Pocket Money} = \frac{1}{100} \times x = \frac{x}{100} \]

3. **Calculate the Elder Son's Share**:
The elder son receives 80% of the total pocket money.
\[ \text{Elder Son's Share} = 80\% \text{ of } \frac{x}{100} = \frac{80}{100} \times \frac{x}{100} = \frac{80x}{10000} \]

4. **Calculate the Elder Son's Expenditure**:
The elder son spends 80% of his share.
\[ \text{Elder Son's Expenditure} = 80\% \text{ of } \frac{80x}{10000} = \frac{80}{100} \times \frac{80x}{10000} = \frac{6400x}{1000000} = \frac{64x}{10000} \]

5. **Calculate the Elder Son's Savings**:
The elder son saves the remaining amount after his expenditure.
\[ \text{Elder Son's Savings} = \text{Elder Son's Share} - \text{Elder Son's Expenditure} \]
\[ = \frac{80x}{10000} - \frac{64x}{10000} = \frac{16x}{10000} \]

6. **Set Up the Equation**:
According to the problem, the elder son saves 20 every month.
\[ \frac{16x}{10000} = 20 \]

7. **Solve for \( x \)**:
Multiply both sides by 10000 to eliminate the fraction:
\[ 16x = 20 \times 10000 \]
\[ 16x = 200000 \]
Now, divide both sides by 16:
\[ x = \frac{200000}{16} = 12500 \]

8. **Final Answer**:
The father's monthly salary is \( \text{Rs. } 12500 \).