Parineeti spends `3/11`th part of her monthly salary on foodgrains and `28%` on jewellery. She invests the remaining part of her salary in mutual fund and stock shares in the ratio 7:5., the investment in mutual fund is Rs 22176, what is her monthly salary ?

Options

A. Rs 82995.12
B. Rs 83995.12
C. Rs 84995.12
D. Rs 80000

Answer

To find Parineeti's monthly salary, we will follow these steps:

### Step 1: Define the monthly salary
Let Parineeti's monthly salary be \( x \).

### Step 2: Calculate the amount spent on foodgrains
Parineeti spends \( \frac{3}{11} \) of her salary on foodgrains. Therefore, the amount spent on foodgrains is:
\[ \text{Amount on foodgrains} = \frac{3}{11} x \]

### Step 3: Calculate the amount spent on jewellery
Parineeti spends \( 28\% \) of her salary on jewellery. Therefore, the amount spent on jewellery is:
\[ \text{Amount on jewellery} = \frac{28}{100} x = 0.28x \]

### Step 4: Calculate the remaining salary
The remaining part of her salary after spending on foodgrains and jewellery is:
\[ \text{Remaining salary} = x - \left(\frac{3}{11} x + 0.28x\right) \]

### Step 5: Simplify the remaining salary
To simplify the expression for the remaining salary:
1. Convert \( 0.28 \) to a fraction: \( 0.28 = \frac{28}{100} = \frac{7}{25} \).
2. Find a common denominator for \( \frac{3}{11} \) and \( \frac{7}{25} \). The least common multiple of \( 11 \) and \( 25 \) is \( 275 \).

Now, convert both fractions:
\[ \frac{3}{11} = \frac{3 \times 25}{11 \times 25} = \frac{75}{275} \]
\[ \frac{7}{25} = \frac{7 \times 11}{25 \times 11} = \frac{77}{275} \]

Now, combine the fractions:
\[ \frac{3}{11} x + 0.28x = \frac{75}{275} x + \frac{77}{275} x = \frac{152}{275} x \]

Thus, the remaining salary is:
\[ \text{Remaining salary} = x - \frac{152}{275} x = \left(1 - \frac{152}{275}\right)x = \frac{123}{275} x \]

### Step 6: Investment in mutual funds and stock shares
Parineeti invests the remaining salary in mutual funds and stock shares in the ratio \( 7:5 \). The total parts of the investment are \( 7 + 5 = 12 \).

### Step 7: Calculate the investment amounts
Let the total amount invested be \( I \):
\[ I = \frac{123}{275} x \]
The amount invested in mutual funds is:
\[ \text{Mutual fund investment} = \frac{7}{12} I = \frac{7}{12} \cdot \frac{123}{275} x \]
We know this amount is \( 22,176 \):
\[ \frac{7}{12} \cdot \frac{123}{275} x = 22,176 \]

### Step 8: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = 22,176 \cdot \frac{12 \cdot 275}{7 \cdot 123} \]

### Step 9: Calculate \( x \)
Calculating the right-hand side:
1. Calculate \( 12 \cdot 275 = 3300 \).
2. Calculate \( 7 \cdot 123 = 861 \).
3. Now substitute:
\[ x = 22,176 \cdot \frac{3300}{861} \]
4. Calculate \( \frac{3300}{861} \approx 3.83 \).
5. Finally, calculate \( x \):
\[ x \approx 22,176 \cdot 3.83 \approx 84,995.12 \]

### Conclusion
Thus, Parineeti's monthly salary is approximately \( \text{Rs } 84,995.12 \).

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