A sum of money is distributed among P, Q, R and S in the ratio 3: 4:5:6, respectively. If R gets Rs 500 more than Q. then the sum of all their shares (in Rs) is:

Options

A. 8000
B. 9000
C. 7500
D. 6000

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Ratio
The ratio of the shares of P, Q, R, and S is given as 3:4:5:6. This means:
- P's share = 3x
- Q's share = 4x
- R's share = 5x
- S's share = 6x

### Step 2: Set Up the Equation
We know that R gets Rs 500 more than Q. Therefore, we can set up the equation:
\[ R = Q + 500 \]
Substituting the expressions for R and Q from the ratio:
\[ 5x = 4x + 500 \]

### Step 3: Solve for x
Now, we can solve for x:
\[ 5x - 4x = 500 \\ x = 500 \]

### Step 4: Calculate Each Share
Now that we have the value of x, we can calculate each person's share:
- P's share = \( 3x = 3 \times 500 = 1500 \)
- Q's share = \( 4x = 4 \times 500 = 2000 \)
- R's share = \( 5x = 5 \times 500 = 2500 \)
- S's share = \( 6x = 6 \times 500 = 3000 \)

### Step 5: Calculate the Total Sum
Now, we can find the total sum of all their shares:
\[ \text{Total} = P + Q + R + S = 1500 + 2000 + 2500 + 3000 \]
Calculating this gives:
\[ \text{Total} = 9000 \]

### Final Answer
The sum of all their shares is Rs 9000.

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