In a partnership, A invests $\frac{1}{6}$ of the capital for $\frac{1}{6}$ of the time, $B$ invests $\frac{1}{3}$ of the capital for $\frac{1}{3}$ of the time and C, the rest of the capital for the whole time. Out of a profit of ₹ 4600, B's share is
(a)₹ 650
(b)₹ 800
(c)₹ 960
(d)₹ 1000
Answer
Answer (as printed): B
Explanation
Suppose A invests ₹ $\frac{x}{6}$ for $\frac{y}{6}$ months. Then, B invests ₹ $\frac{x}{3}$ for $\frac{y}{3}$ months. C invests $\left[x-\left(\frac{x}{6}+\frac{x}{3}\right)\right]$, i.e., $₹ \frac{x}{2}$ for $y$ months. $$\begin{aligned} \therefore \quad & \mathrm{A}: \mathrm{B}: \mathrm{C}=\left(\frac{x}{6} \times \frac{y}{6}\right):\left(\frac{x}{3} \times \frac{y}{3}\right):\left(\frac{x}{2} \times y\right) \\ & =\frac{1}{36}: \frac{1}{9}: \frac{1}{2}=1: 4: 18 . \end{aligned}$$ Hence, B's share $=₹\left(4600 \times \frac{4}{23}\right)=₹ 800$.
Explanation as extracted from the printed page; notation may be imperfect.