Question

A and B are partners in a firm sharing profits and losses in the ratio of 3 : 2. C is admitted into partnership. A sacrifices `1/3` of his share and B `1/10` from his share in favour of C. Determine the sacrificing ratio and the new profit sharing ratio.

Answer 1

Calculation of Sacrificing Ratios:

A’s old share = `3/5`; He surrenders `1/3` of his share

Hence, share surrendered by A = `3/5 xx 1/3`

= `3/15`

= `1/5`

B’s old share = `2/5`; He surrenders `1/10` of his share

Hence, share surrendered by A = `1/10`

= `2/50`

= `1/5`

Sacrifice Ratio = `1/5 : 1/10`

`1/5` = `(1 xx 2)/(5 xx 2)`

= `2/10`

Sacrifice Ratio = `1/5 : 1/10` or 2 : 1

Calculation of New Ratios:

A = `3/5 - 1/5`

= `2/5`

B = `2/5 - 1/10`

= `(2 xx 2)/(5 xx 2) - 1/10`

= `4/10 - 1/10`

= `(4 - 1)/10`

= `3/10`

C = `1/5 + 1/10`

= `(1 xx 2)/(5 xx 2) + 1/10`

= `2/10 + 1/10`

= `(2 + 1)/10`

= `3/10`

New ratio of A, B, and C:

A = `2/5`

= `(2 xx 2)/(5 xx 2)`

= `4/10`

B = `3/10`

C = `3/10`

Hence, New ratio of A, B. and C = `4/10 : 3/10 : 3/10` or 4 : 3 : 3