Question

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 $C$ rest of the capital for whole time.Find $B^{\prime }$s share out of a profit of Rs,$4,600$.

Answer 1

Let x be the total capital invested

Given: $\frac{1}{6}$ of the capital is invested by A

Hence A's investment is $\frac{x}{6}$ for $\frac{T}{6}$ of time.

Hence total value of A's investment for period $T/6=xT/36$

Given: $\frac{1}{3}$ of the capital is invested by b.

Hence 'b's investment is $x/3$ for $T/3$ of time.

Hence, total value of b's investment for period $T/3$ will be $Tx/9$

Rest of the investment is done by c

Hence c's investment is $x-\frac{x}{3}-\frac{x}{6}=\frac{x}{2}$ for period of T.

Hence total value of c's investment for period of T will be $xT/2$

profit should be divided in the total value of investment for period of $T=(\frac{xT}{36}+\frac{xT}{9}+\frac{xT}{2})=\frac{23xT}{36}$

Hence, B's share should be $\frac{xT}{9}/23xT/36=\frac{4}{23}rd$

Hence, profit received by $B=\frac{4}{23}\times 4600=$Rs. $800$.