Manu invested `13%` of his monthly salary in the FD and `12%` in PPF. `3"/"25^(th)` of the remaining amount spent on clothing. `3"/"11^(th)` remaining amount spent on food. `5"/"12^(th)` of remianing spent of education. Half of remaining amount is invested in a scheme which offer `10%` SI from which after 5 year he get 16800 amounts. Find the amount invested in FD and PPF together?

Options

A. 25000
B. 20000
C. 18000
D. None of these

Answer

To solve the problem step by step, we will break down each part of Manu's investments and expenditures.

### Step 1: Determine the Total Salary
Let’s assume Manu's total monthly salary is \( S \).

### Step 2: Calculate the Amount Invested in FD and PPF
- **Investment in FD**: \( 13\% \) of \( S \) = \( 0.13S \)
- **Investment in PPF**: \( 12\% \) of \( S \) = \( 0.12S \)

### Step 3: Calculate the Total Investment in FD and PPF
- Total investment in FD and PPF = \( 0.13S + 0.12S = 0.25S \)

### Step 4: Calculate the Remaining Amount after FD and PPF
- Remaining amount = \( S - (0.13S + 0.12S) = S - 0.25S = 0.75S \)

### Step 5: Calculate the Amount Spent on Clothing
- Amount spent on clothing = \( \frac{3}{25} \) of remaining amount = \( \frac{3}{25} \times 0.75S = \frac{3 \times 0.75}{25}S = \frac{2.25}{25}S = 0.09S \)

### Step 6: Calculate the Remaining Amount after Clothing
- Remaining amount after clothing = \( 0.75S - 0.09S = 0.66S \)

### Step 7: Calculate the Amount Spent on Food
- Amount spent on food = \( \frac{3}{11} \) of remaining amount = \( \frac{3}{11} \times 0.66S = \frac{1.98}{11}S \)

### Step 8: Calculate the Remaining Amount after Food
- Remaining amount after food = \( 0.66S - \frac{1.98}{11}S \)
- To simplify, convert \( 0.66S \) to a fraction: \( 0.66S = \frac{66}{100}S = \frac{33}{50}S \)
- Now, calculate the remaining amount:
\[ \text{Remaining} = \frac{33}{50}S - \frac{1.98}{11}S \]
To subtract these fractions, find a common denominator (which is 550):
\[ \frac{33}{50}S = \frac{33 \times 11}{550}S = \frac{363}{550}S \]
\[ \frac{1.98}{11}S = \frac{1.98 \times 50}{550}S = \frac{99}{550}S \]
\[ \text{Remaining} = \frac{363}{550}S - \frac{99}{550}S = \frac{264}{550}S = \frac{132}{275}S \]

### Step 9: Calculate the Amount Spent on Education
- Amount spent on education = \( \frac{5}{12} \) of remaining amount = \( \frac{5}{12} \times \frac{132}{275}S = \frac{660}{3300}S = \frac{11}{55}S \)

### Step 10: Calculate the Remaining Amount after Education
- Remaining amount after education = \( \frac{132}{275}S - \frac{11}{55}S \)
- Convert \( \frac{11}{55}S \) to a common denominator (275):
\[ \frac{11}{55}S = \frac{11 \times 5}{275}S = \frac{55}{275}S \]
\[ \text{Remaining} = \frac{132}{275}S - \frac{55}{275}S = \frac{77}{275}S \]

### Step 11: Calculate the Amount Invested in the Scheme
- Half of the remaining amount is invested in a scheme:
\[ \text{Investment in scheme} = \frac{1}{2} \times \frac{77}{275}S = \frac{77}{550}S \]

### Step 12: Calculate the Total Amount Received from the Scheme
- The amount received after 5 years is \( 16800 \).
- Using the formula for Simple Interest:
\[ \text{Total Amount} = \text{Principal} + \text{SI} \]
\[ 16800 = \frac{77}{550}S + \left(\frac{77}{550}S \times \frac{10}{100} \times 5\right) \]
\[ 16800 = \frac{77}{550}S + \frac{385}{550}S = \frac{462}{550}S \]
\[ 16800 = \frac{462}{550}S \]
\[ S = 16800 \times \frac{550}{462} \]
\[ S = 20000 \]

### Step 13: Calculate the Amount Invested in FD and PPF
- Total investment in FD and PPF = \( 0.25S = 0.25 \times 20000 = 5000 \)

### Final Answer
The amount invested in FD and PPF together is **5000**.