Out of her monthly salary nupur spends `25%`on house rent and puts 1/3rd in her saving account. Out of the remaining salary , respective ratio between the amount she invest in mutual funds and the amount spent for groceries is 2:3 if amount spent for groceries is 11990 rs, what is nupur 's approximate monthly salary in rs?

Options

A. 36000
B. 56000
C. 52000
D. 48000

Answer

To solve the problem step by step, we will break down Nupur's expenditures and savings based on her monthly salary.

### Step 1: Define the Monthly Salary
Let Nupur's monthly salary be \( S \). For easier calculations, we can express her salary as \( S = 300x \), where \( x \) is a variable we will determine later.

### Step 2: Calculate House Rent
Nupur spends 25% of her salary on house rent. Therefore, the amount spent on house rent is:
\[ \text{House Rent} = 25\% \text{ of } S = \frac{25}{100} \times S = \frac{25}{100} \times 300x = 75x \]

### Step 3: Calculate Savings
Nupur puts 1/3 of her salary into her savings account. Thus, the amount saved is:
\[ \text{Savings} = \frac{1}{3} \text{ of } S = \frac{1}{3} \times 300x = 100x \]

### Step 4: Calculate Remaining Salary
Now, we need to find out how much salary remains after paying for house rent and savings:
\[ \text{Remaining Salary} = S - \text{House Rent} - \text{Savings} = 300x - 75x - 100x = 125x \]

### Step 5: Define the Ratio of Investments
According to the problem, the ratio of the amount invested in mutual funds to the amount spent on groceries is 2:3. Let the amount invested in mutual funds be \( 2y \) and the amount spent on groceries be \( 3y \).

### Step 6: Relate Groceries to Remaining Salary
From the problem, we know that the amount spent on groceries is \( 11990 \) Rs. Therefore:
\[ 3y = 11990 \]
To find \( y \):
\[ y = \frac{11990}{3} \approx 3996.67 \]

### Step 7: Calculate the Total Investment
Now, we can find the total amount represented by \( 5y \) (which is the sum of mutual fund investment and groceries):
\[ 5y = 5 \times 3996.67 \approx 19983.33 \]

### Step 8: Set Up the Equation
Since the remaining salary is \( 125x \) and it equals \( 5y \):
\[ 125x = 19983.33 \]

### Step 9: Solve for \( x \)
To find \( x \):
\[ x = \frac{19983.33}{125} \approx 159.86664 \]

### Step 10: Calculate Nupur's Monthly Salary
Now, substitute \( x \) back into the equation for salary:
\[ S = 300x \approx 300 \times 159.86664 \approx 47960 \]

### Conclusion
Thus, Nupur's approximate monthly salary is:
\[ \text{Monthly Salary} \approx 48000 \text{ Rs} \]