A and B are partners in a business. A contributed \(\frac{1}{3}\) of the capital for 9 months and B received \(\frac{2}{5}\) of the profit. For how long was B's money used in the business?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 months
In a partnership, profit is shared in the ratio of capital × time for each partner.
A’s capital \(=\frac{1}{3}\), so B’s capital \(=\frac{2}{3}\) of the total
B’s share of profit \(=\frac{2}{5}\), so A’s share \(=\frac{3}{5}\); the profit ratio A : B \(=3:2\)
Taking B’s time as \(t\) months: \(\displaystyle\frac{\frac{1}{3}\times9}{\frac{2}{3}\times t}=\frac{3}{2}\)
\(\displaystyle\frac{3}{\frac{2t}{3}}=\frac{9}{2t}=\frac{3}{2}\), so \(6t=18\)
B’s money was used for \(t=3\) months