X and Y are partners sharing profits in 5:3 ratio admitted Z for 1/10 share which he acquired equally for X and Y. Calculate new profit sharing ratio?
New Profit Sharing Ratio of X, Y and Z is 23:13:4
Explanation
This question involves calculating the new profit sharing ratio when a new partner is admitted and acquires his share equally from the existing partners. The key concept is that when a partner acquires share 'equally' from existing partners, the new partner's share is divided equally between the old partners. The old partners surrender a portion of their share to the new partner, and the new ratio is calculated by subtracting the surrendered share from their old share.
Solution Steps
Step 1: Calculate Old Shares of X and Y Old Profit Sharing Ratio of X and Y = 5:3 X's share = 5/8 Y's share = 3/8
Step 2: Calculate Share Surrendered to Z Z's share = 1/10 (acquired equally from X and Y) Share acquired from X = 1//2 = 1/20 Share acquired from Y = 1//2 = 1/20
Step 3: Calculate New Shares X's new share = Old share – Share surrendered = 5/8 – 1/20 = 25/40 – 2/40 = 23/40
Y's new share = Old share – Share surrendered = 3/8 – 1/20 = 15/40 – 2/40 = 13/40
Z's share = 1/10 = 4/40
Step 4: Calculate New Profit Sharing Ratio X : Y : Z = 23/40 : 13/40 : 4/40 New Profit Sharing Ratio = 23:13:4