 ### In a partnership, A invests $\Large\frac{1}{6}$ of the capital $\Large\frac{1}{6}$ for of the time, B invests $\Large\frac{1}{3}$ of the capital for $\Large\frac{1}{3}$ of the time and C, the rest of the capital for the whole time. Out of a profit of Rs. 4600, B’s share is ?

A. Rs. 650 B. Rs. 800 C. Rs. 960 D. Rs. 1000 Answer: Option B
\begin{aligned}&\text{Suppose}\\ &\text{A invests Rs. }\frac{x}{6}\text{ for }\frac{y}{6}\text{ months}\\ &\text{Then,}\\ &\text{ B invests Rs. }\frac{x}{3}\text{ for }\frac{y}{3}\text{ months }\\ &\text{ C invests }\left[x-\left(\frac{x}{6}+\frac{x}{3}\right)\right]\\ &\text { i.e., Rs. } \frac{x}{2} \text { for } y \text { months }\end{aligned} \begin{aligned}&\therefore\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} \begin{aligned}&\text{Hence, B’s share}\\ &=\text{ Rs. }\left(4600\times\frac{4}{23}\right)\\ &=\text{ Rs. }800\end{aligned}