Question : A sum of money is to be divided among P, Q, and R in the ratio 7 : 9 : 4. If P gets Rs. 1500 more than R then find the difference between the shares of P and Q.
Option 1: Rs. 1,500
Option 2: Rs. 900
Option 3: Rs. 1,000
Option 4: Rs. 500
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Correct Answer: Rs. 1,000
Solution :
Let the common ratio be $x$.
Share of P = $7x$
Share of Q = $9x$
Share of R = $4x$
Difference = Share of P – Share of Q
Given that P receives Rs. 1500 more than R:
So, $7x - 4x =1500$
⇒ $3x = 1500$
⇒$x = 500$
The difference between the shares of P and Q:
Difference = Share of Q – Share of P = $9x-7x = 2x$
= Rs. 4500 – Rs. 3500
= Rs. 1,000
Therefore, the difference between the shares of P and Q is Rs. 1,000.
Hence, the correct answer is Rs. 1,000.
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