If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their…

Concept: In a partnership problem, when the question does not mention different time periods for the partners, the standard convention is to assume all partners invested their capital for the same length of time. Under that assumption, profit is shared strictly in proportion to the capital invested — that is, Profit ratio = Capital ratio (since profit share is proportional to Capital multiplied by Time, and Time cancels out when it is equal for everyone).

Working:

1. The two profit shares given are Rs.400 and Rs.600, so the profit ratio is 400 : 600.

2. Divide both terms by their greatest common factor, 200: 400/200 : 600/200 = 2 : 3.

3. As no separate time periods are mentioned, taking the standard assumption of equal investment duration, the capital ratio equals this profit ratio, so the ratio of their capitals is 2 : 3.

Check: If the capitals were in the ratio 2k : 3k for some k, and both were invested for the same time, the profits would also be in the ratio 2k : 3k = 2 : 3, which matches the given profit shares 400 : 600 = 2 : 3 exactly.