X and Y are two partners sharing profits in the ratio of 3:1. Z is admitted for 1/8th share of profits. Calculate the new profit-sharing ratio of X, Y, and Z.
Answers
Old ratio (X and Y) = 3 : 1
Z is admitted for 1/3 share
Let the combined share of profit for all partners after Z's admission = 1
Combined share of X and Y after Z's admission = 1 - Z's share
= 1 - (1/3)
= 2/3
New ratio = Old ratio * Combined share of X and Y
X's new share = (3/4) * (2/3)
= 2/4
Y's new share = (1/4) * (2/3)
= 1/6
Z's share = 1/3
Therefore, new share of X, Y and Z = (2/4), (1/6) and (1/3)
= (6/12), (2/12) and (4/12)
= 6 : 2 : 4 or 3 : 1 : 2
Explanation:
★ Old Ratio :
X : Y = 3 : 1
- X's Share = 3/4
- Y's Share = 1/4
Z is admitted for 1/8th share of profits.
- Z's Share = 1/8
Let,
Total Profit of all Partners = 1
- Z's Share = 1/8
Remaining Share =
1 - 1/8 = 7/8
★ New Profit Sharing Ratio :
• X's New Share =
⇒ 3/4 × 7/8 = 21/32
• Y's New Share =
⇒ 1/4 × 7/8 = 7/32
• Z's Share =
⇒ 1/8 = (1×4)/(8×4)
⇒ 4/32
New Profit Sharing Ratio =
- X : Y : Z
- 21/32 : 7/32 : 4/32
⇒ 21 : 7 : 4
Therefore,
New Profit Sharing Ratio =
X : Y : Z = 21 : 7 : 4