A started a business by investing ₹76,000. After a few months B joined him and invested ₹57,000. At the end of the year, the total profit was divided between A and B in the ratio 2 : 1. For how many months B remained in the business?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
In a partnership, profit is shared in the ratio of capital × time for each partner. A’s money stayed in the business for all 12 months; let B’s stay for \(m\) months.
A’s capital-months: \(76000\times12\); B’s capital-months: \(57000\times m\)
These are in the profit ratio 2 : 1: \(\displaystyle \frac{76000\times12}{57000\times m}=\frac{2}{1}\)
The capitals are in the ratio \(\displaystyle \frac{76000}{57000}=\frac{4}{3}\), so \(\displaystyle \frac{4\times12}{3m}=2\)
Then \(48=6m\), so \(m=8\)