Question

A and B share profits in the ratio of 3 : 2. They agreed to admit C on the condition that A will sacrifice `3/25`th of his share of profit in favour of C and B will sacrifice `1/25`th of his profits in favour of C. The new profit-sharing ratio will be ______.

Options

• 12 : 9 : 4

• 3 : 2 : 4

• 66 : 48 : 11

• 48 : 66 : 11

Answer 1

A and B share profits in the ratio of 3 : 2. They agreed to admit C on the condition that A will sacrifice `3/25`th of his share of profit in favour of C and B will sacrifice `1/25`th of his profits in favour of C. The new profit-sharing ratio will be 66 : 48 : 11.

Explanation:

Calculate the amount of sacrifice from each partner:

Old shares = 3 : 2

A’s sacrifice = `3/25 xx 3/5`

= `9/125`

B’s sacrifice = `1/25 xx 2/5`

= `2/125`

Calculate the new share of each partner:

A’s new share = `3/5 - 9/125`

= `(3 xx 25)/(5 xx 25) - 9/125`

= `75/125 - 9/125`

= `66/125`

B’s new share = `2/5 - 2/125`

= `(2 xx 25)/(5 xx 25) - 2/125`

= `50/125 - 2/125`

= `48/125`

C’s share = A’s sacrifice + B’s sacrifice

= `9/125 + 2/125`

= `11/125`

The new profit-sharing ratio for A, B, and C = `66/125 : 48/125 : 11/125` or 66 : 48 : 11.