Question

A sum of money is distributed among four people P, Q, R, and S in the ratio 2 : 5 : 4 : 3. If Q gets Rs. 2000 more than S, then what will be the total amount?

• A. 18000
• B. 16000
• C. 14000
• D. 15000

Hint:

When working with ratios, use the relationship between the parts to form an equation, then solve for the total.

Answer 1

The Correct Option is C

Let the total sum be \( x \). According to the given ratio, the amounts received by P, Q, R, and S are proportional to 2, 5, 4, and 3, respectively. So, the shares of P, Q, R, and S are: \[ \frac{2}{14}x, \frac{5}{14}x, \frac{4}{14}x, \frac{3}{14}x \] We are told that Q gets Rs. 2000 more than S, so: \[ \frac{5}{14}x - \frac{3}{14}x = 2000 \] Simplifying: \[ \frac{2}{14}x = 2000 \] \[ \frac{1}{7}x = 2000 \] Multiplying both sides by 7: \[ x = 14000 \] Thus, the total amount is \( \boxed{14000} \).