A man spends 40% of his monthly salary on food and one-third of the remaining on transport. If he saves 4,500 per month, which is equal to half the balance after spending on food and transport, his monthly salary is

Options

A. A) 11250
B. B) 22500
C. C) 25000
D. D) 45000

Answer

To solve the problem step by step, let's denote the monthly salary of the man as \( S \).

### Step 1: Calculate the amount spent on food
The man spends 40% of his salary on food. Therefore, the amount spent on food can be calculated as:
\[ \text{Amount spent on food} = 0.40 \times S \]

### Step 2: Calculate the remaining salary after food
After spending on food, the remaining salary can be calculated as:
\[ \text{Remaining salary} = S - 0.40S = 0.60S \]

### Step 3: Calculate the amount spent on transport
The man spends one-third of the remaining salary on transport. Therefore, the amount spent on transport is:
\[ \text{Amount spent on transport} = \frac{1}{3} \times (0.60S) = 0.20S \]

### Step 4: Calculate the total amount spent
The total amount spent on both food and transport can be calculated as:
\[ \text{Total amount spent} = \text{Amount spent on food} + \text{Amount spent on transport} = 0.40S + 0.20S = 0.60S \]

### Step 5: Calculate the balance after spending on food and transport
The balance after spending on food and transport is:
\[ \text{Balance} = S - \text{Total amount spent} = S - 0.60S = 0.40S \]

### Step 6: Relate savings to the balance
According to the problem, the man saves ₹4,500, which is equal to half of the balance after spending on food and transport. Therefore, we can set up the equation:
\[ 4500 = \frac{1}{2} \times (0.40S) \]

### Step 7: Solve for \( S \)
To find \( S \), we can multiply both sides of the equation by 2:
\[ 9000 = 0.40S \]
Now, divide both sides by 0.40:
\[ S = \frac{9000}{0.40} = 22500 \]

### Conclusion
The monthly salary of the man is ₹22,500.

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