Satish saves 10% of his monthly salary . And of the remaining salary `(1)/(3) th and (1)/(2)th` he gives to his mother and sister respectively and the remaining salary he submits as his EMI for the payment of his car . If his annual EMI was Rs. 50,000, then find his monthly salary ?

Options

A. Rs. 33,000
B. Rs. 27,000
C. Rs. 32,000
D. Rs. 27,800

Explanation

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

### Step-by-Step Solution:

1. **Assume Monthly Salary**:
Let's assume Satish's monthly salary is \( S \).

2. **Calculate Savings**:
Satish saves 10% of his monthly salary. Therefore, his savings can be calculated as:
\[ \text{Savings} = 0.10 \times S = 0.1S \]

3. **Calculate Remaining Salary**:
After saving, the remaining salary is:
\[ \text{Remaining Salary} = S - \text{Savings} = S - 0.1S = 0.9S \]

4. **Distribute Remaining Salary**:
Satish gives \( \frac{1}{3} \) of the remaining salary to his mother and \( \frac{1}{2} \) of the remaining salary to his sister.
- Amount given to mother:
\[ \text{Mother's Share} = \frac{1}{3} \times 0.9S = 0.3S \]
- Amount given to sister:
\[ \text{Sister's Share} = \frac{1}{2} \times 0.9S = 0.45S \]

5. **Calculate Total Amount Given Away**:
The total amount given to both mother and sister is:
\[ \text{Total Given Away} = 0.3S + 0.45S = 0.75S \]

6. **Calculate Remaining Amount for EMI**:
The remaining amount after giving to his mother and sister is:
\[ \text{Remaining for EMI} = 0.9S - 0.75S = 0.15S \]

7. **Set Up the EMI Equation**:
We know that Satish's annual EMI is Rs. 50,000. Therefore, the monthly EMI is:
\[ \text{Monthly EMI} = \frac{50000}{12} = 4166.67 \]
This amount is equal to the remaining salary he has after giving to his mother and sister:
\[ 0.15S = 4166.67 \]

8. **Solve for S**:
To find \( S \), we can rearrange the equation:
\[ S = \frac{4166.67}{0.15} = 27777.78 \]

9. **Final Calculation**:
Rounding to the nearest whole number, Satish's monthly salary is approximately:
\[ S \approx 27800 \]

### Conclusion:
Satish's monthly salary is approximately Rs. 27,800.