Question

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets ₹1000 more than S, what is the share of Q (in ₹)?

• A. 500
• B. 1000
• C. 1500
• D. 2000

Hint:

When distributing a sum of money in a given ratio, first find the total number of parts, then calculate the value of each part and finally the share of each person.

Answer 1

The Correct Option is D

Let the total sum be represented by \( x \). The shares of P, Q, R, and S are in the ratio 5:2:4:3. The total number of parts is: \[ 5 + 2 + 4 + 3 = 14 \text{ parts}. \] So, the value of one part is: \[ \frac{x}{14}. \] Now, it is given that R gets ₹1000 more than S. So, the difference between R's and S's share is: \[ 4\left(\frac{x}{14}\right) - 3\left(\frac{x}{14}\right) = \frac{x}{14}. \] This difference is ₹1000: \[ \frac{x}{14} = 1000. \] Solving for \( x \): \[ x = 1000 \times 14 = 14000. \] Now, the share of Q is: \[ 2\left(\frac{14000}{14}\right) = 2 \times 1000 = 2000. \] Thus, the share of Q is ₹2000.