A,B and C are partners sharing profits in the ratio of 8:7:5. D is admitted as a new partner for 1/4th share. B sacrifice 1/10th from his share in favour of D and the remaining sacrifice made by A and C in the ratio 2:1. Calculate sacrificing ratio amd new profit sharing ratio?

Question

Answer

Given:

Profit sharing ratio of A, B and C is 8:7:5 respectively

D is admitted as a new partner for 1/4th share

B sacrifices 1/10th from his share in favour of D

A and C make remaining sacrifice in the ratio 2:1

To Find:

Sacrificing ratio

New profit sharing ratio

Solution:

Step 1: Calculation of B's sacrifice

Let the total profit be x

Partner's profit share before D's admission is {8/20}x, {7/20}x and {5/20}x for A, B and C respectively

B sacrifices 1/10th from his share in favour of D

New profit share of B after sacrifice is {7/20}x - {1/10}({7/20}x) = {3/20}x

Step 2: Calculation of total sacrifice and A and C's sacrifice

Total sacrifice is 1/4th + 1/10th = 3/20th

Ratio of A and C's sacrifice = 2:1

Let A's sacrifice be 2x and C's sacrifice be x

So, 2x + x = 3/20th

x = 3/60th = 1/20th

A's sacrifice = 2(1/20th) = 1/10th and C's sacrifice = 1/20th

Step 3: Calculation of sacrificing ratio

Sacrificing ratio of A, B and C = 1/10th : 1/20th : 1/20th = 2:1:1

Step 4: Calculation of new profit sharing ratio

After D's admission, total profit sharing ratio becomes 8:7:5:1

Let D's share be x

So, {3/20}x = {7/20}x - x

x = {7/40}x

Therefore, D's share = 1/6th

New profit sharing ratio = 8:7:5:1/6 = 48:42:30:1

Therefore, the sacrificing ratio is 2:1:1 and the new profit sharing ratio is 48:42:30:1.

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