A father want to divide Rs. 22,515 among his four sons P, Q, R and S such that `("P's share")/("Q's share") =("Q's share")/("R's share") = ("R's share")/("S's share") = 1/2 ` . Find the share of Q.

Options

A. 1507
B. 3002
C. 6004
D. `12,008`

Explanation

To solve the problem of dividing Rs. 22,515 among the four sons P, Q, R, and S in the given ratio, we can follow these steps:

### Step 1: Understand the Ratios
The ratios given are:
- \( \frac{P}{Q} = \frac{1}{2} \)
- \( \frac{Q}{R} = \frac{1}{2} \)
- \( \frac{R}{S} = \frac{1}{2} \)

This means:
- \( Q = 2P \)
- \( R = 2Q \)
- \( S = 2R \)

### Step 2: Express All Shares in Terms of P
From the ratios, we can express all shares in terms of P:
- \( Q = 2P \)
- \( R = 2Q = 2(2P) = 4P \)
- \( S = 2R = 2(4P) = 8P \)

So, we have:
- \( P = P \)
- \( Q = 2P \)
- \( R = 4P \)
- \( S = 8P \)

### Step 3: Write the Total Share Equation
Now, we can write the total amount shared among the sons:
\[ P + Q + R + S = 22,515 \]
Substituting the expressions in terms of P:
\[ P + 2P + 4P + 8P = 22,515 \]
\[ 15P = 22,515 \]

### Step 4: Solve for P
To find P, divide both sides by 15:
\[ P = \frac{22,515}{15} = 1,501 \]

### Step 5: Calculate Q's Share
Now that we have P, we can find Q:
\[ Q = 2P = 2 \times 1,501 = 3,002 \]

### Final Answer
The share of Q is Rs. 3,002.

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