A certain amount is divided among P, Q and R in the ratio of 3 : 7 : 6 respectively. If the difference between share of P and Q is Rs. 2700, what is R's share?

Options

A. A) Rs. 4050
B. B) Rs. 2121
C. C) Rs. 5040
D. D) Rs. 3550

Answer

To solve the problem, we need to find R's share when the total amount is divided among P, Q, and R in the ratio of 3:7:6, and the difference between the shares of P and Q is Rs. 2700.

### Step-by-Step Solution:

1. **Understanding the Ratio**:
The shares of P, Q, and R are in the ratio of 3:7:6. This means:
- P's share = 3x
- Q's share = 7x
- R's share = 6x
where x is a common multiplier.

2. **Finding the Difference**:
We know that the difference between the shares of P and Q is Rs. 2700. Therefore, we can set up the equation:
\[ Q's \, share - P's \, share = 2700 \]
Substituting the values we have:
\[ 7x - 3x = 2700 \]

3. **Simplifying the Equation**:
Simplifying the left side gives:
\[ 4x = 2700 \]

4. **Solving for x**:
To find the value of x, we divide both sides by 4:
\[ x = \frac{2700}{4} = 675 \]

5. **Calculating R's Share**:
Now that we have the value of x, we can find R's share:
\[ R's \, share = 6x = 6 \times 675 = 4050 \]

6. **Final Answer**:
Therefore, R's share is Rs. 4050.

### Summary of the Solution:
- P's share = 3x
- Q's share = 7x
- R's share = 6x
- Difference between Q and P = Rs. 2700
- Solving gives x = 675
- R's share = 6x = Rs. 4050