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 $C,$ the rest of the capital for the whole time. Out of a profit of $4600$ rupees, share of $B$ is

• A. $650$ rupees
• B. $800$ rupees
• C. $960$ rupees
• D. $1000$ rupees

Answer 1

The correct option is B $800$ rupees

Suppose $A$ invests $\frac{x}{6}$ rupees for $\frac{y}{6}$ months.
Then, $B$ invests $\frac{x}{3}$ rupees for $\frac{y}{3}$ months.
$C$ invests $[x-(\frac{x}{6}+\frac{x}{3})]=\frac{x}{2}$ rupees for $y$ months.
$\therefore A:B:C=(\frac{x}{6}\times \frac{y}{6}):(\frac{x}{3}\times \frac{y}{3}):(\frac{x}{2}\times y)=\frac{1}{36}:\frac{1}{9}:\frac{1}{2}=1:4:18$
Hence, share of $B$ is $(4600\times \frac{4}{23})=800$ rupees