Question

$P,Q$ and $R$ are partners in a business .$P$ whose money has been used for $4$ months , claims $\frac{1}{8}$ of the profit , $Q$ whose money has been used for $6$ months ,claims at $\frac{1}{3}$ of the profit . $R$ had invested Rs. $1560$ for $8$ months .How much did $P$ and $Q$ contribute ?

Answer 1

Let P and Q invested $2x$ and $2y$ respectively P's profit $=\frac{1}{8}$ and Q's profit $=\frac{1}{3}$

$\therefore$ R's profit $=1-(\frac{1}{8}+\frac{1}{3})=1-\frac{11}{24}=\frac{24-11}{24}$

$=\frac{13}{24}$

P's share: Q's share : R's share

$=\frac{1}{8}:\frac{1}{3}:\frac{13}{24}$

$\Rightarrow \frac{4x}{12}:\frac{6y}{12}:1560\times \frac{8}{12}=3:8:13$

$\Rightarrow 2x:3y:6240=3:8:13$

$\Rightarrow \frac{2x}{6240}=\frac{3}{13}$

$\Rightarrow 2x=\frac{3\times 6240}{13}$

$\Rightarrow 2x=480\times 3$

$\Rightarrow x=240\times 3=$Rs. $720$/-

and $\frac{3y}{6240}=\frac{8}{13}$

$\Rightarrow y=\frac{6240\times 3}{3\times 13}$

$y=\frac{480\times 8}{3}=1280$/-

Thus P invested Rs. $720$/- and Q invested Rs. $1280$/-.