A man spends `10%` of his monthly salary on house rent and `20%` of the rest on education of the children and `25%` of the rest on other expenditures . Thus he saves `Rs.3645`. Find the total monthly salary ?

Options

A. Rs. `6550`
B. Rs. `6850`
C. Rs. `6750`
D. Rs. `6650`

Answer

To find the total monthly salary of the man, we can break down the problem step by step.

### Step 1: Define the Monthly Salary
Let the total monthly salary be \( S \).

### Step 2: Calculate House Rent
The man spends 10% of his salary on house rent:
\[ \text{House Rent} = 0.10 \times S = 0.1S \]

### Step 3: Calculate Remaining Salary After Rent
After paying the house rent, the remaining salary is:
\[ \text{Remaining Salary} = S - 0.1S = 0.9S \]

### Step 4: Calculate Education Expenses
He spends 20% of the remaining salary on education:
\[ \text{Education Expenses} = 0.20 \times (0.9S) = 0.18S \]

### Step 5: Calculate Remaining Salary After Education
After paying for education, the remaining salary is:
\[ \text{Remaining Salary} = 0.9S - 0.18S = 0.72S \]

### Step 6: Calculate Other Expenditures
He spends 25% of the remaining salary on other expenditures:
\[ \text{Other Expenditures} = 0.25 \times (0.72S) = 0.18S \]

### Step 7: Calculate Remaining Salary After All Expenditures
After all expenditures, the remaining salary (which is his savings) is:
\[ \text{Savings} = 0.72S - 0.18S = 0.54S \]

### Step 8: Set Up the Equation
We know that his savings amount to Rs. 3645:
\[ 0.54S = 3645 \]

### Step 9: Solve for \( S \)
To find \( S \), divide both sides by 0.54:
\[ S = \frac{3645}{0.54} = 6750 \]

### Final Answer
The total monthly salary is:
\[ \boxed{6750} \]

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