P and Q are partners sharing profits in 2:1 ratio. They admitted R into partnership giving him 1/5 share which he acquired from P and Q in 1:2 ratio. Calculate new profit sharing ratio?
New Profit Sharing Ratio is 3:1:1.
Explanation
The new partner R acquires his share from the old partners in a specific ratio (1:2), rather than their old profit sharing ratio. Therefore, we must calculate the specific portion of profit surrendered by each old partner to R. P's new share is calculated by deducting the portion acquired by R from P's old share, and similarly for Q. The resulting shares are then simplified to find the final ratio.
Solution Steps
Old Profit Sharing Ratio of P and Q is 2:1. P's Share = 2/3 Q's Share = 1/3
R's Share is given as 1/5. R acquires this share from P and Q in the ratio of 1:2.
Calculation of Share Acquired by R: Share acquired from P = (1/3) of (1/5) = 1/15 Share acquired from Q = (2/3) of (1/5) = 2/15
Calculation of New Shares: P's New Share = Old Share - Share Acquired by R = 2/3 - 1/15 = 10/15 - 1/15 = 9/15
Q's New Share = Old Share - Share Acquired by R = 1/3 - 2/15 = 5/15 - 2/15 = 3/15
R's Share = 1/5 = 3/15
New Profit Sharing Ratio: P : Q : R 9/15 : 3/15 : 3/15 = 9 : 3 : 3 = 3 : 1 : 1