Pankaj and Sushil invested some amount of money in the ratio of 3: 5for the same period in a business. They decided that at the end of year `20% `profit was to be given to AIDS Control Society of India as a donation. Out of the remaining, `75%` was to be reinvested and the rest of die profit was to be divided as interest on their capitals. If the difference in their shares is ₹ 1200. Find the total profit?

Options

A. ₹ 18000
B. ₹ 24000
C. ₹ 20000
D. none of these

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Understand the Investment Ratio
Pankaj and Sushil invested in the ratio of 3:5. This means if Pankaj invested 3 parts, Sushil invested 5 parts.

### Step 2: Calculate Total Parts
The total parts of the investment = 3 + 5 = 8 parts.

### Step 3: Determine the Profit Distribution
At the end of the year, the total profit is to be divided as follows:
- 20% of the total profit is donated to AIDS Control Society.
- The remaining 80% of the profit is available for reinvestment and distribution.

### Step 4: Calculate the Amount Reinvested
Out of the remaining 80% profit:
- 75% is reinvested.
- Therefore, the amount distributed among Pankaj and Sushil is 25% of the remaining profit.

### Step 5: Set Up the Equation for Shares
Let the total profit be \( P \).
- The amount donated = \( 0.20P \)
- Remaining profit = \( 0.80P \)
- Amount reinvested = \( 0.75 \times 0.80P = 0.60P \)
- Amount distributed = \( 0.25 \times 0.80P = 0.20P \)

### Step 6: Calculate Individual Shares
The remaining profit of \( 0.20P \) is divided between Pankaj and Sushil based on their investment ratio (3:5).
- Total ratio parts = 3 + 5 = 8 parts.
- Pankaj's share = \( \frac{3}{8} \times 0.20P \)
- Sushil's share = \( \frac{5}{8} \times 0.20P \)

### Step 7: Find the Difference in Shares
According to the problem, the difference in their shares is ₹1200.
- Difference = Sushil's share - Pankaj's share
- \( \frac{5}{8} \times 0.20P - \frac{3}{8} \times 0.20P = 1200 \)

### Step 8: Simplify the Equation
- \( \left(\frac{5 - 3}{8} \times 0.20P\right) = 1200 \)
- \( \frac{2}{8} \times 0.20P = 1200 \)
- \( \frac{1}{4} \times 0.20P = 1200 \)
- \( 0.05P = 1200 \)

### Step 9: Solve for Total Profit
- \( P = \frac{1200}{0.05} = 24000 \)

### Final Answer
The total profit is ₹24000.

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