Question

A and B were partners in a firm sharing profits in the ratio of 3 : 2. C and D were admitted as new partners. A sacrificed `1/4`th of his share in favour of C and B sacrificed 50% of his share in favour of D. Calculate the new profit-sharing ratio of A, B, C and D.

Answer 1

A’s old share = `3/5` and sacrifices = `1/4`

Sacrifice by A  = `3/5 xx 1/4`

= `3/20`

A’s new share = `3/5 - 3/20`

= `3/5 xx 4/4`

= `12/20`

= `12/20 - 3/20`

= `9/20`

B’s old share = `2/5` and sacrifices 50% = `1/2`

Sacrifice by B  = `2/5 xx 1/2`

= `2/10`

= `1/5`

B’s new share = `2/5 - 1/5`

= `1/5`

The new partners’ shares are equal to the sacrifices made by the old partners.

C's share (from A’s sacrifice) = `3/20`

D’s share (from B’s sacrifice) = `1/5`

To find the ratio, find a common denominator, which is 20.

A = `9/20`

B = `1/5`

= `(1 xx 4)/(5 xx 4)`

= `4/20`

C = `3/20`

D = `1/5`

= `(1 xx 4)/(5 xx 4)`

= `4/20`

The new profit-sharing ratio `9/20 : 4/20 : 3/20 : 4/20` or 9 : 4 : 3 : 4