A, B and C enter into a partnership. A contributes one-third of the capital while B contributes as much as A and C together contribute. If the profit at the end of the year amounts to ₹ 900, what would C receive?
(a)₹ 100
(b)₹ 150
(c)₹ 200
(d)₹ 300
Answer
Answer (as printed): B
Explanation
Let total capital $=₹ x$. Then, A's capital $=₹\left(\frac{x}{3}\right)$. $$\begin{aligned} \text { B's capital } & =(\mathrm{A}+\mathrm{C}) \text { 's capital } \Rightarrow 2 \text { (B's capital) } \\ & =(\mathrm{A}+\mathrm{B}+\mathrm{C}) \text { 's capital }=₹ x \end{aligned} \begin{aligned} & \text { ⇒ B's capital }=₹\left(\frac{x}{2}\right) . \\ & \text { C's capital }=₹\left[x-\left(\frac{x}{3}+\frac{x}{2}\right)\right]=₹ \frac{x}{6} . \\ & \therefore \quad \text { A }: \text { B }: \text { C }=\frac{x}{3}: \frac{x}{2}: \frac{x}{6}=2: 3: 1 . \\ & \text { So, C's share }=₹\left(900 \times \frac{1}{6}\right)=₹ 150 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.