ifferent Cases of NPS) X, Y and Z were partners sharing in 4 : 3 : 3 ratio. Z retired and his re was taken over by:x entirely, (ii) Y entirely, (ii) X and Y equally, (iv) X and Y in 1 : 2 ratio. Calculate New Ratio. . (i) 7:3: (ii) 2:3; (iii) 11:9, (iv) 1:1]
Answers
Given:
- X, Y and Z were partners in a firm, sharing profits and losses in the ratio 4:3:3.
- Z retired.
To find: The new ratio.
Answer:
Case 1: When Z's share is taken by X entirely
New share = Old share + Retiring partner's share
Since X takes all of Z's share, i.e., 3/10, it will be added to X's share, i.e., 4/10.
- X's new ratio = 4/10 + 3/10 = 7/10
Y's ratio remains the same.
Therefore, the new profit-sharing ratio is 7:3.
Case 2: When Z's share is taken by Y entirely
New share = Old share + Retiring partner's share
It's the same as in the above case, but instead of X, we take Y. Since Y takes all of Z's share, i.e., 3/10, it will be added to Y's share, i.e., 3/10.
- Y's new ratio = 3/10 + 3/10 = 6/10
X's ratio remains the same.
Therefore, the new profit-sharing ratio is 4:6, or 2:3.
Case 3: When Z's share is taken by X and Y equally
New share = Old share + Gain from retiring partner's share
This means that Z's share, i.e., 3/10, will need to be divided into 2, since there are 2 partners remaining after the retirement.
This implies that X and Y get 3/10 × 1/2 = 3/20 each.
- X's new ratio = 4/10 + 3/20 = (8 + 3)/20 = 11/20
- Y's new ratio = 3/10 + 3/20 = (6 + 3)/20 = 9/20
Therefore, the new profit-sharing ratio is 11:9.
Case 4: When Z's share is taken by X and Y in the ratio 1:2
New share = Old share + Gain from retiring partner's share
This means that Z's share, i.e., 3/10, will be divided among X and Y in the ratio of 1:2.
From Z, X gets:
- 3/10 × 1/3 = 3/30
From Z, Y gets:
- 3/10 × 2/3 = 6/30
- X's new ratio = 4/10 + 3/30 = (12 + 3)/30 = 15/30
- Y's new ratio = 3/10 + 6/30 = (9 + 6)/30 = 15/30
Therefore, the new profit-sharing ratio is 1:1.