Question

P and Q are partners sharing profits in the ratio of 3 : 2. They admit R into partnership who acquires 1/5th of his share from P and 4/25th share from Q. Calculate New Profit-sharing Ratio and Sacrificing Ratio.

Answer 1

Calculation of New Profit Sharing Ratio
= P : Q = 3 : 2 (Old Ratio)
R acquires `1/5`th of his share from P
And, Remaining `4/5 th(1 - 1/5)` of his share from Q
If `4/5`th share of R = `4/25`
R's Share = `4/25 xx 5/4 = 5/25`

P's Sacrifice = `1/5 xx 1/5 = 1/25`

Q's Sacrifice = `4/25`

P's new Share = `3/5 - 1/25 = [ 15 - 1 ]/25 = 14/25`

Q's new share = `2/5 - 4/25 = [ 10 - 4 ]/25 = 6/25`

R's new share = `1/5 xx 5/5 = 5/25`

P : Q : R = 14 : 6 : 5

Sacrificing ratio = 1 : 4