Question

A, B and Care partners with capitals of ₹ 1,00,000; ₹ 75,000 and ₹ 50,000 respectively. On C's retirement, his share is acquired by A and B in the ratio of 6 : 4. Ascertain new profit sharing ratio and gaining ratio.

Answer 1

1. Gaining Ratio

The problem states that C's share is acquired by A and B in the ratio of 6 : 4.

Gaining Ratio = 6 : 4, which simplifies directly to 3 : 2

2. Calculation of New Profit Sharing Ratio

Old Ratio:

Since no explicit profit ratio is given, the old ratio is equal:

A : B : C = 1 : 1 : 1

C's retiring share = `1/3`

Share Gained by Remaining Partners:

Share gained by A = `1/3 xx 6/10 = 6/30`

Share gained by A = `1/3 xx 4/10 = 4/30`

New Share of A and B:

A's New Share = Old Share + Gained Share

`1/3 + 6/30 = 10/30 + 6/30 = 16/30`

B's New Share = Old Share + Gained Share

`1/3 + 4/30 = 10/30 + 4/30 = 14/30`

New Profit Sharing Ratio:

Ratio between A and B = 16 : 14

Dividing both sides by 2 gives 8 : 7