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

Let payments be $a,b,c,d$ with total $S=60$. A's condition: $a=\tfrac{1}{2}(S-a)$ $\Rightarrow$ $2a=S-a$ $\Rightarrow$ $3a=S$ $\Rightarrow$ $a=20$.
B's condition: $b=\tfrac{1}{3}(S-b)$ $\Rightarrow$ $3b=S-b$ $\Rightarrow$ $4b=S$ $\Rightarrow$ $b=15$.
C's condition: $c=\tfrac{1}{4}(S-c)$ $\Rightarrow$ $4c=S-c$ $\Rightarrow$ $5c=S$ $\Rightarrow$ $c=12$.
Then $d=S-(a+b+c)=60-(20+15+12)=\boxed{13}$.