Question

P, Q, R and S were partners sharing profits in the ratio of 2 : 3 : 5 : 2. S retires and his share is acquired by Q and R in the ratio of 3 : 2. Calculate new ratio and gaining ratio.

Answer 1

Old ratio = P : Q : R : S = 2 : 3 : 5 : 2

S's share = `2/12 = 1/6`

S's share is acquired by Q and R in the ratio 3 : 2.

Q's gain = `1/6 xx 3/5 = 1/10`

R's gain = `1/6 xx 2/5 = 1/15`

Gaining Ratio

`1/10 : 1/15 = 3 : 2`

New Ratio

P = `2/12 = 1/6`

Q = `3/12 + 1/10 = 13/30`

R = `5/12 + 1/15 = 9/20`

Taking LCM 60:

P : Q : R = 10 : 26 : 27

New Profit-Sharing Ratio = 10 : 26 : 27

Gaining Ratio (Q : R) = 3 : 2