A,B and C invest in the ratio of 3: 4: 5. The percentage of return on their investments are in the ratio of 6: 5: 4. Find the total earnings, if B earns ₹ 250 more than A :

Options

A. ₹ 6000
B. ₹ 7250
C. ₹ 5000
D. none of these

Answer

To solve the problem step by step, we need to find the total earnings of A, B, and C based on their investments and returns.

### Step 1: Define the investments
Let the investments of A, B, and C be represented as:
- A's investment = 3x
- B's investment = 4x
- C's investment = 5x

### Step 2: Define the returns
Let the returns on their investments be represented as:
- A's return = 6y
- B's return = 5y
- C's return = 4y

### Step 3: Set up the equation based on the information given
According to the problem, B earns ₹250 more than A. Therefore, we can set up the equation:
\[ 5y = 6y + 250 \]

### Step 4: Solve the equation
Rearranging the equation gives us:
\[ 5y - 6y = 250 \]
\[ -y = 250 \]
\[ y = -250 \]

However, since y cannot be negative in this context, we need to reconsider our returns. The correct equation should be:
\[ 6y - 5y = 250 \]
This simplifies to:
\[ y = 250 \]

### Step 5: Calculate the returns for A, B, and C
Now that we have y, we can find the returns for A, B, and C:
- A's return = 6y = 6 * 250 = ₹1500
- B's return = 5y = 5 * 250 = ₹1250
- C's return = 4y = 4 * 250 = ₹1000

### Step 6: Calculate the total earnings
Now we can find the total earnings:
\[ \text{Total earnings} = A's return + B's return + C's return \]
\[ = 1500 + 1250 + 1000 = ₹3750 \]

### Final Answer
The total earnings of A, B, and C is ₹3750.

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