A sum of Rs 3,900 is divided among P, Q and R such that R receives two-fifths of P's share and Q receives three times of R's share. What is Q's share (in Rs)?

Options

A. 1500
B. 600
C. 1800
D. 1200

Answer

To solve the problem step by step, we start by defining the shares of P, Q, and R based on the information given in the question.

### Step 1: Define the shares
Let P's share be denoted as \( P \), R's share as \( R \), and Q's share as \( Q \). According to the problem:
- R receives two-fifths of P's share:
\[ R = \frac{2}{5}P \]
- Q receives three times R's share:
\[ Q = 3R \]

### Step 2: Express Q in terms of P
Substituting the expression for R into the equation for Q:
\[ Q = 3R = 3 \left( \frac{2}{5}P \right) = \frac{6}{5}P \]

### Step 3: Write the total sum equation
The total sum of money distributed among P, Q, and R is Rs 3900. Therefore, we can write:
\[ P + Q + R = 3900 \]
Substituting the expressions for Q and R:
\[ P + \frac{6}{5}P + \frac{2}{5}P = 3900 \]

### Step 4: Combine the terms
To combine the terms, we first convert all terms to have a common denominator:
\[ P + \frac{6}{5}P + \frac{2}{5}P = \frac{5}{5}P + \frac{6}{5}P + \frac{2}{5}P = \frac{13}{5}P \]
Thus, we have:
\[ \frac{13}{5}P = 3900 \]

### Step 5: Solve for P
To find P, multiply both sides by 5:
\[ 13P = 3900 \times 5 \]
\[ 13P = 19500 \]
Now, divide by 13:
\[ P = \frac{19500}{13} = 1500 \]

### Step 6: Calculate R's share
Now that we have P's share, we can calculate R's share:
\[ R = \frac{2}{5}P = \frac{2}{5} \times 1500 = 600 \]

### Step 7: Calculate Q's share
Finally, we can calculate Q's share:
\[ Q = 3R = 3 \times 600 = 1800 \]

### Conclusion
Thus, Q's share is Rs 1800.