Question

A, B and C enter into a partnership and their shares are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$. After $2$ months A withdraws half of his capital and after $10$ months a profit of Rs $378$ is divided among them. What is Bs share?

• A. Rs $129$
• B. Rs $144$
• C. Rs $156$
• D. Rs $168$

Answer 1

The correct option is B Rs $144$

$A:B:C=\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ L.C.M of $2,3$ and $4=12$

$=(\frac{1}{2}\times 12):(\frac{1}{3}\times 12):(\frac{1}{4}\times 12)$

$=6:4:3$

Total profit=Rs$378$

For $2$ month $\to A:B:C=6:4:3$

After $2$ months $A$ withdraw half of his capital

For next $10$ months $\to A:B:C=3:4:3$

Total money ratio $\to A:B:C=6:4:3$

$\to A:B:C=\{(6\times 2)+(3\times 10)\}:\{(4\times 2)+(4\times 10)\}:\{(3\times 2)+(3\times 10)\}=42:48:36=7:8:6$

Sum of ratio$=7+8+6=21$

$\therefore B$'s share$=\frac{8}{21}\times$ Rs $378$=Rs$144$