Amrit invests 30% of his monthly salary on house rent and 20% of remaining in food. Again, he invested 25% of the remaining in mutual fund. If he invested rs. 5600 in mutual fund and food then his monthly salary is:

Options

A. a. 20,000
B. b. 25000
C. c. 30000
D. d.none of these

Answer

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

### Step 1: Calculate the amount spent on house rent
Amrit invests 30% of his monthly salary on house rent. Therefore, the amount spent on house rent is:
\[ \text{House Rent} = 0.30 \times S \]

### Step 2: Calculate the remaining amount after house rent
After paying the house rent, the remaining amount is:
\[ \text{Remaining after House Rent} = S - \text{House Rent} = S - 0.30S = 0.70S \]

### Step 3: Calculate the amount spent on food
Amrit then spends 20% of the remaining amount on food. Thus, the amount spent on food is:
\[ \text{Food} = 0.20 \times (0.70S) = 0.14S \]

### Step 4: Calculate the remaining amount after food
After spending on food, the remaining amount is:
\[ \text{Remaining after Food} = 0.70S - 0.14S = 0.56S \]

### Step 5: Calculate the amount spent on mutual funds
Amrit invests 25% of the remaining amount in mutual funds. Therefore, the amount spent on mutual funds is:
\[ \text{Mutual Fund} = 0.25 \times (0.56S) = 0.14S \]

### Step 6: Set up the equation based on the total investment in food and mutual funds
According to the problem, the total amount spent on food and mutual funds is Rs. 5600. Therefore, we can write:
\[ \text{Food} + \text{Mutual Fund} = 0.14S + 0.14S = 0.28S = 5600 \]

### Step 7: Solve for \( S \)
To find the monthly salary \( S \), we can rearrange the equation:
\[ 0.28S = 5600 \]
\[ S = \frac{5600}{0.28} = 20000 \]

### Conclusion
Thus, Amrit's monthly salary is:
\[ \boxed{20000} \]