Two businessmen A and B invest in a business in the ratio 5 : 8. They decided to reinvest `30%` of the profit they earned back into the business. The remaining profit they distributed amongst themselves. If A's share of the profit was Rs 87,500 then how much profit (in Rs) did the business make?

Options

A. 227000
B. 250000
C. 375000
D. 325000

Answer

To solve the problem step by step, let's follow the reasoning based on the information given:

### Step 1: Understand the Investment Ratio
The investment ratio of A to B is given as 5:8. This means that for every 5 parts A invests, B invests 8 parts.

### Step 2: Calculate the Total Parts of Investment
The total parts of investment can be calculated as:
\[ \text{Total Parts} = 5 + 8 = 13 \]

### Step 3: Determine A's Share of the Total Investment
A's share of the total investment can be expressed as:
\[ \text{A's Share} = \frac{5}{13} \]

### Step 4: Determine B's Share of the Total Investment
Similarly, B's share of the total investment is:
\[ \text{B's Share} = \frac{8}{13} \]

### Step 5: Let the Total Profit be P
Let the total profit made by the business be \( P \).

### Step 6: Calculate the Amount Reinvested
According to the problem, 30% of the profit is reinvested back into the business. Therefore, the amount reinvested is:
\[ \text{Reinvested Amount} = 0.30P \]

### Step 7: Calculate the Remaining Profit
The remaining profit, which is distributed among A and B, is:
\[ \text{Remaining Profit} = P - 0.30P = 0.70P \]

### Step 8: Calculate A's Share of the Remaining Profit
Since A's share of the profit is Rs 87,500, we can express A's share of the remaining profit as:
\[ \text{A's Share of Remaining Profit} = \frac{5}{13} \times 0.70P \]
Setting this equal to Rs 87,500 gives us:
\[ \frac{5}{13} \times 0.70P = 87,500 \]

### Step 9: Solve for P
To find \( P \), we can rearrange the equation:
\[ 0.70P = 87,500 \times \frac{13}{5} \]
Calculating the right side:
\[ 0.70P = 87,500 \times 2.6 = 227,500 \]
Now, divide both sides by 0.70:
\[ P = \frac{227,500}{0.70} = 325,000 \]

### Final Answer
Thus, the total profit made by the business is:
\[ \text{Total Profit} = Rs 325,000 \]