Question

A, B, and C are partners sharing profits in 9 : 6 : 5. D is admitted into partnership. A sacrifices `1/3`rd of his share, B sacrifices `1/20`th from his share, and C sacrifices `1/5`th of his share in favour of D. The New profit-sharing ratio will be ______.

Options

• 7 : 15 : 12 : 26

• 5 : 6 : 4 : 5

• 6 : 5 : 1 : 8

• 6 : 5 : 4 : 5

Answer 1

A, B, and C are partners sharing profits in 9 : 6 : 5. D is admitted into partnership. A sacrifices `1/3`rd of his share, B sacrifices `1/20`th from his share, and C sacrifices `1/5`th of his share in favour of D. The New profit-sharing ratio will be 6 : 5 : 4 : 5.

Explanation:

Calculate the Sacrifice Ratio:

A sacrifices `1/3`rd of his share.

A’s sacrifices = `9/20 xx 1/3`

= `9/60`

A sacrifices `1/20` from his share. This is an absolute amount, not a fraction of his share.

B’s sacrifices = `1/20`

C’s sacrifices = `1/5`of his share.

C’s sacrifices = `5/20 xx 1/5`

= `5/100`

To combine these fractions, we find a common denominator.

A’s Sacrifice = `9/60`

= `(9 xx 5)/(60 xx 5)`

= `45/300`

B’s Sacrifice = `1/20`

= `(1 xx 15)/(20 xx 15)`

= `15/300`

C’s sacrifices = `5/100`

= `(5 xx 3)/(100 xx 3)`

= `15/300`

The Sacrifice Ratio of A, B, and C = `45/300 : 15/300 : 15/300` or 45 : 15 : 15

Calculate the New Share for Each Partner:

A’s New Share = `9/20 - 45/300`

= `(9 xx 15)/(20 xx 15) - 45/300`

= `135/300 - 45/300`

= `90/300`

B’s New Share = `6/20 - 15/300`

= `(6 xx 15)/(20 xx 15) - 15/300`

= `90/300 - 15/300`

= `75/300`

C’s New Share = `5/20 - 15/300`

= `(5 xx 15)/(20 xx 15) - 15/300`

= `75/300 - 15/300`

= `60/300`

C’s Share = `45/300 + 15/300 + 15/300`

= `75/300`

The New Profit Sharing Ratio of A, B, C, D = `90/300 : 75/300 : 60/300 : 5/300`

We can simplify this ratio by dividing all numbers by their greatest common divisor, which is 15.

The New Profit Sharing Ratio of A, B, C, D = `6/20 : 5/20 : 4/20 : 5/20` or 6 : 5 : 4 : 5