Marhumu and Yusuf are in partnership sharing profits and losses in the ratio of 2:1. On 31/3/2000, the partnership decided to admit Idris who is to take 1/4...

Marhumu and Yusuf are in partnership sharing profits and losses in the ratio of 2:1. On 31/3/2000, the partnership decided to admit Idris who is to take 1/4 of future profits without changing the ratio of Marhumu and Yusuf.

What is the new profit-sharing ratio of Marhumu and Yusuf?

Answer Details

Before admitting Idris, Marhumu and Yusuf shared the profits and losses in the ratio of 2:1, which can be represented as 2/3 for Marhumu and 1/3 for Yusuf. Now Idris is to take 1/4 of future profits without changing the ratio of Marhumu and Yusuf. This means that the remaining profits will be shared between Marhumu and Yusuf in the same ratio of 2:1 as before. The new profit-sharing ratio of Marhumu and Yusuf can be calculated as follows: Let x be the share of the remaining profits that Idris does not take. Then, Marhumu's share will be 2/3 of x, and Yusuf's share will be 1/3 of x. Since Idris is taking 1/4 of the total profits, his share can be represented as 1/4, or 1/4 = x/(x + 3/4). Solving for x, we get x = 3/16. Therefore, Marhumu's share is 2/3 of 3/16, which is 1/8, or 12.5%. And Yusuf's share is 1/3 of 3/16, which is 1/16, or 6.25%. So the new profit-sharing ratio of Marhumu and Yusuf is 12.5% : 6.25%, which can be simplified to 50% : 25%. Hence, the correct option is 50% : 25%.