Out of his monthly salary, Dhiren invested `30%` in mututal funds.. From his remaining salary .he paid `20%` towards house-rent and the respective ratio between his expenses .towards house-rent, .grocery and medicine was 7:12:8. If Dhiren was left with ₹4400,what was his monthly salary?

Options

A. 27500
B. 25500
C. 28000
D. 26000

Answer

To solve the problem step by step, we will denote Dhiren's monthly salary as \( S \).

### Step 1: Calculate the amount invested in mutual funds
Dhiren invested 30% of his salary in mutual funds.
\[ \text{Investment in mutual funds} = 0.30 \times S \]

### Step 2: Calculate the remaining salary after investment
The remaining salary after the investment is:
\[ \text{Remaining salary} = S - 0.30S = 0.70S \]

### Step 3: Calculate the house rent expense
Dhiren paid 20% of his remaining salary towards house rent.
\[ \text{House rent} = 0.20 \times (0.70S) = 0.14S \]

### Step 4: Set up the ratio of expenses
The ratio of Dhiren's expenses towards house rent, grocery, and medicine is given as 7:12:8. Let the common multiple be \( x \). Thus, we can express the expenses as:
- House rent = \( 7x \)
- Grocery = \( 12x \)
- Medicine = \( 8x \)

### Step 5: Relate house rent to the total expenses
From Step 3, we know that:
\[ 7x = 0.14S \]
To find \( x \):
\[ x = \frac{0.14S}{7} = 0.02S \]

### Step 6: Calculate grocery and medicine expenses
Now we can calculate the expenses for grocery and medicine:
- Grocery = \( 12x = 12 \times 0.02S = 0.24S \)
- Medicine = \( 8x = 8 \times 0.02S = 0.16S \)

### Step 7: Calculate total expenses
The total expenses can now be calculated as:
\[ \text{Total expenses} = \text{House rent} + \text{Grocery} + \text{Medicine} + \text{Mutual funds} \]
\[ \text{Total expenses} = 0.14S + 0.24S + 0.16S + 0.30S = 0.84S \]

### Step 8: Calculate savings
Dhiren's savings are given as ₹4400, which can be expressed as:
\[ \text{Savings} = S - \text{Total expenses} = S - 0.84S = 0.16S \]
Setting this equal to ₹4400:
\[ 0.16S = 4400 \]

### Step 9: Solve for \( S \)
To find \( S \):
\[ S = \frac{4400}{0.16} = 27500 \]

### Final Answer
Dhiren's monthly salary is ₹27,500.

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