A, B and C are partners, and the profit is shared in the ratio of their capitals. A receives \(\frac{2}{3}\) of the profit, and B and C divide the remaining profit equally. If A's income increases by ₹400 when the rate of profit rises from 5% to 7%, what is the capital of B?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹5,000
The profit is shared in the ratio of the capitals, so each partner's share of the profit is also his share of the capital. The rate of profit is reckoned on the total capital.
The shares (from the division of profit):
A: \(\frac{2}{3}\); the remaining \(\frac{1}{3}\) is split equally, so B: \(\frac{1}{6}\) and C: \(\frac{1}{6}\)
The total capital (the rise in the rate is 7% − 5% = 2%):
Rise in the total profit \(=2\%\) of the total capital
A's part of that rise: \(\frac{2}{3}\times2\%\) of the total capital \(=400\)
So \(2\%\) of the total capital \(=600\), and the total capital \(=30000\)
B's capital:
\(\frac{1}{6}\times30000=5000\)