Question

$A,B$ and $C$ started a business where their initial capital was in the ratio of $4:5:6$. At the end of $8$ months, $A$ invested an amount such that his total capital became half to $C^{\prime }$s initial capital investment. If the annual profit of $B$ is Rs. $7500$ then what is the total profit ?

Answer 1

Initial Ratio $=4:5:6$

$A^{\prime }$s share for $8$ months $=4\times 8$

$A^{\prime }$s share for $4$ months $=3\times 4$ (half of $C^{\prime }$s share)

Thus their total share:

$\Rightarrow 4\times 8+3\times 4:5\times 12:6\times 12$

$\Rightarrow 44:60:72$

$\Rightarrow 11:15:18$

Let total profit be $x$

$B^{\prime }$s profit is Rs $7500$

Thus,

$\Rightarrow \frac{15}{11+15+18}\times x=7500$

$\Rightarrow \frac{15x}{44}=7500$

$\Rightarrow x=22000$

$\therefore$ Total profit $=22000$ Rs.