Question

Find New Profit-sharing Ratio:
A and B are partners sharing profits and losses in the ratio of 3 : 2. They admit C for 1/5th share in the profit. C acquires 1/5th of his share from A and 4/5th share from B.

Answer 1

Old Ratio = A : B 
                 = 3 : 2
C admits for `1/5` share of profit

A's Sacrifice = C's share x `1/5`

                    = `1/5 xx 1/5 = 1/25`

B's Sacrifice = C's share x `4/5`

                    = `1/5 xx 4/5 = 4/25`

New Ratio = Old Ratio − Sacrificing Ratio

A's = `3/5 - 1/25 = 14/25`

B's = `2/5 - 4/25 = 6/25`

New Profit Sharing Ratio = A : B : C 
                                        = `14/25 : 6/25 : 1/5`

                                       = ` [ 14 : 6 : 5 ]/25`

                                       = 14 : 6 : 5