A, B and C are partners in a business. A, whose money has been used for 4 months, claims of the profit. 8 1 B, whose money has been used for 6 months, claims of the profit. C had invested ` 1560 for 8 months. 3 How much money did A and B contribute?
Answer
Answer (as printed):
Explanation
Let the total profit be ₹$x$. Then, A's share $=₹\frac{x}{8}$; B's share $=₹\frac{x}{3}$; C's share $=₹\left[x-\left(\frac{x}{8}+\frac{x}{3}\right)\right]=₹\left(x-\frac{11x}{24}\right)=₹\left(\frac{13x}{24}\right)$. $\therefore$ Ratio of shares of A, B and C $=\frac{x}{8}:\frac{x}{3}:\frac{13x}{24}=3:8:13$. Suppose A invested ₹$y$ for 4 months and B invested ₹$z$ for 6 months. Then, $\frac{y\times4}{1560\times8}=\frac{3}{13} \Rightarrow 52y=37440 \Rightarrow y=720$. And, $\frac{z\times6}{1560\times8}=\frac{8}{13} \Rightarrow 78z=99840 \Rightarrow z=1280$. Hence, A's contribution $=₹720$; B's contribution $=₹1280$.
Explanation as extracted from the printed page; notation may be imperfect.