A sum of ₹ 2236 is divided among A, B and C in such a way that A receives 25\% more than C and C receives 25\% less than B. What is A's share in the amount?
(a)₹ 460
(b)₹ 780
(c)₹ 890
(d)₹ 1280
(e)None of these
Answer
Answer (as printed): B
Explanation
Let the amount received by $B$ be ₹ $x$. Then, amount received by $C=75 \%$ of $₹ x=₹ \frac{3 x}{4}$. And, amount received by $A=125 \%$ of $₹ \frac{3 x}{4}=₹ \frac{15 x}{16}$. $$\begin{aligned} & \therefore \frac{15 x}{16}+x+\frac{3 x}{4}=2236 \Rightarrow \frac{43 x}{16}=2236 \\ & \Rightarrow x=\left(\frac{2236 \times 16}{43}\right)=832 . \end{aligned}$$ Hence, A's share $=₹\left(\frac{15}{16} \times 832\right)=₹ 780$.
Explanation as extracted from the printed page; notation may be imperfect.