4. X and Y are partners sharing profits and losses in the ratio of 3:2...
Solution:
Given,
X and Y are partners sharing profits and losses in the ratio of 3:2.
Z is a new partner who gets 1/5th share.
Step 1: Calculation of New Share
Let the total profit be P.
Then, Z's share in profit = P/5
Step 2: Calculation of New Ratio
(i) If Z acquires his share from X and Y in their profit sharing ratio
Z acquires the share in the ratio of 3:2.
Let Z's share be P/5 = 2x.
Then, X's share = 3x and Y's share = 2x.
Therefore, the new profit sharing ratio will be 3x+2x : 2x : 2x = 5x : 2x : 2x = 5:2:2.
(ii) If he acquires 3/20th from X and 1/20th from Y
Let Z's share be P/5 = 4x.
Then, X's share = 3x - 3/20 P and Y's share = 2x - 1/20 P.
Therefore, the new profit sharing ratio will be (3x-3/20 P) : (2x-1/20 P) : 4x = (15x-3/4 P) : (10x-1/4 P) : 16x.
(iii) If he acquires 1/10th from X and 1/10th from Y
Let Z's share be P/5 = 2x.
Then, X's share = 3x-1/10 P and Y's share = 2x-1/10 P.
Therefore, the new profit sharing ratio will be (3x-1/10 P) : (2x-1/10 P) : 2x = (15x-P/10) : (10x-P/10) : 10x.
(iv) If he acquires 1/20th from X and 3/20th from Y
Let Z's share be P/5 = 4x.
Then, X's share = 3x-1/20 P and Y's share = 2x-3/20 P.
Therefore, the new profit sharing ratio will be (3x-1/20 P) : (2x-3/20 P) : 4x = (15x-P/5) : (10x-3/5 P) : 16x.
Thus, the new profit sharing ratio can be calculated based on the share acquired by Z from X and Y.