Question

Find out the sacrificing ratio and new ratio in the following case:

A and B are partners sharing profits and losses in the ratio of 4 : 3. C is admitted for 1/5th share. A and B decided to share equally in future. Calculate the new ratio and sacrificing ratio.

Answer 1

Given:

Old ratio of A and B = 4 : 3

C is admitted for 1/5 share

A and B will share the remaining profit equally

1. New Ratio

C gets: `1/5`

Remaining share for A and B: `1 - 1/5 = 4/5`

Since A and B share this equally:

A = `2/5, B = 2/5`

Therefore, the new ratio is:

`2/5 : 2/5 : 1/5`

Multiplying by 5:

2 : 2 : 1

2. Sacrificing Ratio

Old shares: `A = 4/7, B = 3/7`

New shares: `A = 2/5, B = 2/5`

A's sacrifice:

`4/7 - 2/5 = (20 - 14)/35 = 6/35`

B's sacrifice:

`3/7 - 2/5 = (15 - 14)/35 = 1/35`

Thus, sacrificing ratio:

`6/35 : 1/35 = 6 : 1`