Question

A, B and C are partners sharing profits and losses in the ratio of 4 : 3 : 2. C died. A takes `4/9` of C’s share and balance is taken by В.

Calculate the New Profit-sharing Ratio and Gaining Ratio.

Answer 1

Old Ratio (A : B : C) = 4 : 3 : 2

A’s Gain: A takes `4/9` of C’s share.

A’s Gain = `4/9 xx 2/9`

= `8/81`

B’s Gain:

B takes the balance of C’s share = `1 - 4/9`

= `5/9`

B’s Gain = `5/9 xx 2/9`

= `10/81`

Comparing the gained shares of A and B `(8/81 : 10/81)`, 

The Gaining Ratio is 8 : 10, which simplifies to 4 : 5.

Convert the old shares to a common denominator of 81:

A’s Old Share = `4/9 = (4 xx 9)/(9 xx 9)`

= `36/81`

B’s Old Share = `3/9 = (3 xx 9)/(9 xx 9)`

= `27/81`

Now apply the formula:

New Share = Old Share + Gaining Share

A’s New Share = `36/81 + 8/81`

= `44/81`

B’s New Share = `27/81 + 10/81`

= `37/81`

The New Profit-sharing Ratio between A and B is 44 : 37.