Question

R and S are partners in a 4:1 ratio. T is admitted and gets 1/5 share, equally from both. Find the new ratio.

• A. 16:4:5
• B. 8:2:5
• C. 4:1:5
• D. 3:2:5

Hint:

When a new partner is admitted, the existing partners' shares are diluted to accommodate the new partner’s share. The shares are adjusted based on the existing profit-sharing ratio.

Answer 1

The Correct Option is A

R and S are currently sharing profits in a 4:1 ratio. When T is admitted, he gets 1/5 of the total share, and this share will be equally distributed between R and S.
- T’s share = \( \frac{1}{5} \)
Thus, the remaining share is \( 1 - \frac{1}{5} = \frac{4}{5} \).
Since R and S share this remaining \( \frac{4}{5} \) in the ratio of 4:1, we need to split the remaining share between R and S.
The total parts of the ratio = \( 4 + 1 = 5 \).
Thus, the share for R is: \[ \frac{4}{5} \times \frac{4}{5} = \frac{16}{25} \] The share for S is: \[ \frac{1}{5} \times \frac{4}{5} = \frac{4}{25} \] Therefore, the new ratio of R, S, and T is: \[ R : S : T = \frac{16}{25} : \frac{4}{25} : \frac{1}{5} = 16 : 4 : 5 \] Thus, the new profit-sharing ratio is 16:4:5.