A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 15%, he is only able to save Rs. 400 per month. What is his monthly salary ?

Options

A. a. 5000
B. b. 4500
C. c. 6000
D. d. 6500

Explanation

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

### Step 1: Define Variables
Let the monthly salary of the man be \( S \).

### Step 2: Calculate Savings
According to the problem, the man saves 20% of his monthly salary. Therefore, his savings can be expressed as:
\[ \text{Savings} = 0.2S \]

### Step 3: Calculate Monthly Expenses
If the man saves 20% of his salary, then his monthly expenses can be calculated as:
\[ \text{Expenses} = S - \text{Savings} = S - 0.2S = 0.8S \]

### Step 4: Increase in Expenses
Due to the increase in the cost of living, his expenses increase by 15%. Thus, the new expenses can be calculated as:
\[ \text{New Expenses} = \text{Expenses} + 0.15 \times \text{Expenses} = 0.8S + 0.15 \times 0.8S = 0.8S \times (1 + 0.15) = 0.8S \times 1.15 = 0.92S \]

### Step 5: New Savings Calculation
After the increase in expenses, the man is only able to save Rs. 400 per month. Therefore, we can express his new savings as:
\[ \text{New Savings} = S - \text{New Expenses} = S - 0.92S = 0.08S \]
According to the problem, this is equal to Rs. 400:
\[ 0.08S = 400 \]

### Step 6: Solve for Monthly Salary
To find the monthly salary \( S \), we can rearrange the equation:
\[ S = \frac{400}{0.08} = 5000 \]

### Final Answer
The monthly salary of the man is Rs. 5000.

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