Question

A, B, C and D purchase a gift worth ₹60. A pays $\tfrac{1}{2}$ of what others are paying, B pays $\tfrac{1}{3}$ of what others are paying, and C pays $\tfrac{1}{4}$ of what others are paying. What is the amount paid by D? 

• A. ₹14
• B. ₹15
• C. ₹16
• D. ₹13

Hint:

Phrases like "pays $\frac{1}{k}$ of what others are paying" translate to $x=\frac{1}{k}(S-x)$ where $S$ is the total. Solve each to get $x$ directly.

Answer 1

The Correct Option is D

Step 1: \(A=\tfrac{S}{3}\), \(B=\tfrac{S}{4}\), \(C=\tfrac{S}{5}\) (each from "pays a fraction of what others pay").

Step 2: \(D\)'s fraction of total: \[ \frac{D}{S}=1-\left(\frac13+\frac14+\frac15\right)=\frac{13}{60} \]

Step 3: With \(S=60\): \[ D=60\times\frac{13}{60}=\boxed{₹13} \]