A and B invest in a business in the ratio of `3:2`. If 5% of the total profit goes to a charity and A's share is Rs4275, then what will be the total profit ?

Options

A. Rs8000
B. Rs7700
C. Rs7500
D. Rs6500

Answer

To find the total profit based on the information given, we can follow these steps:

### Step 1: Understand the Ratio of Investment
A and B invest in the business in the ratio of 3:2. This means that for every 3 parts that A invests, B invests 2 parts.

### Step 2: Calculate A's Share in Terms of Units
Since A's share is given as Rs 4275, we can denote A's investment as 3 units and B's investment as 2 units. Thus, we can say:
- A's share (3 units) = Rs 4275

### Step 3: Find the Value of One Unit
To find the value of one unit, we divide A's share by the number of units A has:
\[ \text{Value of 1 unit} = \frac{4275}{3} = 1425 \text{ Rs} \]

### Step 4: Calculate B's Share
B's share is represented by 2 units. Therefore, we can calculate B's share as:
\[ \text{B's share} = 2 \times 1425 = 2850 \text{ Rs} \]

### Step 5: Calculate Total Investment of A and B
Now, we can find the total investment of A and B together:
\[ \text{Total investment (A + B)} = \text{A's share} + \text{B's share} = 4275 + 2850 = 7125 \text{ Rs} \]

### Step 6: Determine the Profit Percentage
Since 5% of the total profit goes to charity, A and B together receive 95% of the total profit. Therefore, we can denote the total profit as \( P \):
\[ 0.95P = 7125 \]

### Step 7: Solve for Total Profit
To find the total profit \( P \), we rearrange the equation:
\[ P = \frac{7125}{0.95} \]
Calculating this gives:
\[ P = 7500 \text{ Rs} \]

### Final Answer
The total profit is Rs 7500.

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