Question

A, B and C were in partnership sharing profits in the ratio of 4 : 3 : 1. The partners agreed to share future profits in the ratio of 5 : 4 : 3. Calculate each partner's gain or sacrifice due to change in ratio.

Answer 1

Old ratio:

A : B : C = 4 : 3 : 1

Total parts:

4 + 3 + 1 = 8

So old shares are:

`A = 4/8, B = 3/8, C = 1/8`

New ratio:

A : B : C = 5 : 4 : 3

Total parts:

5 + 4 + 3 = 12

So new shares are:

`A = 5/12, B = 4/12, C = 3/12`

To find gain or sacrifice, use:

Sacrifice = Old Share − New Share

If the answer is positive, the partner sacrifices. If it is negative, the partner gains.

For A:

`4/8 - 5/12`

LCM of 8 and 12 is 24:

`4/8 = 12/24`

`5/12 = 10/24`

Therefore:

`12/24 - 10/24 = 2/24`

So,

A sacrifices `2/24`

For B:

`3/8 - 4/12`

Convert both to denominator 24:

`3/8 = 9/24`

`4/12 = 8/24`

Therefore:

`9/24 - 8/24 = 1/24`

So,

B sacrifices `1/24`

For C:

`1/8 - 3/12`

Convert to denominator 24:

`1/8 = 3/24`

`3/12 = 6/24`

Therefore:

`3/24 - 6/24 = -3/24`

The negative sign means C has gained.

So,

C gains `3/24`