Question

A and B are partners in a firm sharing profits in the ratio of 3 : 1. They admit C and decide that the profit-sharing ratio between B and C shall be same as existing between A and B. Calculate new profit-sharing ratio and the sacrificing ratio.

Answer 1

Calculate new profit-sharing ratio:

The ratio between A and B is 3 : 1. Hence, the ratio between B and C should also be the same i.e., 3 : 1 (or `B = 3/4, C = 1/4`)

Thus, If the ratio of B is 3, the ratio of C should be = 1

In the A : B ratio, B’s share is 1 part.

In the B : C ratio, B’s share is 3 parts.

The lowest common multiple of 1 and 3 is 3.

Let’s convert the ratios to have a common B component:

Multiply the A:B ratio (3 ∶ 1) by 3:

A’s share = 3 × 3

= 9

B’s share = 1 × 3

= 3

The B : C ratio 3 ∶ 1 is already in terms of 3 parts for B.

A : B : C = 9 : 3 : 1

A’s new share = `9/13`

B’s new share = `3/13`

C’s new share = `1/13`

The new profit-sharing ratio = 9 : 3 : 1

Calculate the Sacrificing Ratio:

Sacrificing Share = Old Share − New Share

A = `3/4 - 9/13`

= `(3 xx 13)/(4 xx 13) - (9 xx 4)/(13 xx 4)`

= `39/52 - 36/52`

= `(39 - 36)/52`

= `3/52`

A = `1/4 - 3/13`

= `(1 xx 13)/(4 xx 13) - (3 xx 4)/(13 xx 4)`

= `13/52 - 13/52`

= `(13 - 12)/52`

= `1/52`

Sacrificing Ratio of A and B = `3/52 : 1/52` or 3 : 1