A, B and C enter into partnership with capitals of ` 25000, ` 30000 and ` 15000 respectively. A is the working partner and he gets 30% of the profit for managing the business. The balance profit is distributed in proportion to the capital investment. At the year-end, A gets ` 200 more than B and C together. Find the total profit and the share of each.
Answer
Answer (as printed):
Explanation
Let the total profit be ₹$x$. Amount obtained by A for managing $=₹\left(\frac{30x}{100}\right)=₹\left(\frac{3x}{10}\right)$. Balance profit $=₹\left(x-\frac{3x}{10}\right)=₹\left(\frac{7x}{10}\right)$. Ratio of capitals $=25000:30000:15000=5:6:3$. $\therefore$ A's share $=₹\left[\left(\frac{7x}{10}\times\frac{5}{14}\right)+\frac{3x}{10}\right]=₹\left(\frac{11x}{20}\right)$; B's share $=₹\left(\frac{7x}{10}\times\frac{6}{14}\right)=₹\left(\frac{3x}{10}\right)$; C's share $=₹\left(\frac{7x}{10}\times\frac{3}{14}\right)=₹\left(\frac{3x}{20}\right)$. $\therefore \frac{3x}{10}+\frac{3x}{20}+200=\frac{11x}{20} \Rightarrow x=2000$. So, total profit $=₹2000$. $\therefore$ A's share $=₹\left(\frac{11\times2000}{20}\right)=₹1100$; B's share $=₹\left(\frac{3\times2000}{10}\right)=₹600$; C's share $=₹\left(\frac{3\times2000}{20}\right)=₹300$.
Explanation as extracted from the printed page; notation may be imperfect.