A certain sum of money was distributed among P, R and S in the ratio 5:7:9 respectively. If the difference between the distributed money of P and S is Rs. 2500. What is that certain sum of money?

Options

A. Rs. 1312
B. Rs. 13525
C. Rs. 13125
D. Rs. 23125

Answer

To solve the problem, we need to find the total sum of money distributed among P, R, and S, given that their shares are in the ratio of 5:7:9 and the difference between the amounts received by P and S is Rs. 2500.

### Step-by-Step Solution:

1. **Define the Shares**:
Let the shares of P, R, and S be represented as:
- P's share = 5x
- R's share = 7x
- S's share = 9x

2. **Set Up the Equation**:
According to the problem, the difference between the amounts received by S and P is Rs. 2500:
\[ S - P = 2500 \]
Substituting the values of S and P:
\[ 9x - 5x = 2500 \]

3. **Simplify the Equation**:
Simplifying the left side gives:
\[ 4x = 2500 \]

4. **Solve for x**:
To find the value of x, divide both sides by 4:
\[ x = \frac{2500}{4} = 625 \]

5. **Calculate Individual Shares**:
Now that we have the value of x, we can find the individual shares:
- P's share = \(5x = 5 \times 625 = 3125\)
- R's share = \(7x = 7 \times 625 = 4375\)
- S's share = \(9x = 9 \times 625 = 5625\)

6. **Calculate Total Sum of Money**:
The total sum of money distributed among P, R, and S is:
\[ \text{Total} = P + R + S = 5x + 7x + 9x = 21x \]
Substituting the value of x:
\[ \text{Total} = 21 \times 625 = 13125 \]

### Final Answer:
The certain sum of money distributed among P, R, and S is Rs. 13,125.

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