Question

A, B, C, and D are in partnership sharing profits and losses in the ratio of 9 : 6 : 5 : 5. E joins the partnership for a 20% share. A. B, C and D would in the future share profits among themselves as `3/10 : 4/10 : 2/10 : 1/10`. The new profit-sharing ratio will be ______.

Options

• 3 : 4 : 2 : 1 : 5

• 9 : 6 : 5 : 5 : 5

• 6 : 8 : 4 : 2 : 5

• 8 : 6 : 4 : 2 : 5

Answer 1

A, B, C, and D are in partnership sharing profits and losses in the ratio of 9 : 6 : 5 : 5. E joins the partnership for a 20% share. A. B, C and D would in the future share profits among themselves as `3/10 : 4/10 : 2/10 : 1/10`. The new profit-sharing ratio will be 6 : 8 : 4 : 2 : 5.

Explanation:

E joins the partnership for a 20% share, which is equivalent to `20/100 "or" 1/5` of the total profit.

The remaining share of profit to be distributed among the old partners A, B, C, D is:

1 − E’s share = `1 - 1/5`

= `4/5`

Their new individual shares are calculated by applying this new ratio to the remaining `4/5` share: 

A’s new share = `3/10 xx 4/5`

= `12/50`

B’s new share = `4/10 xx 4/5`

= `16/50`

C’s new share = `2/10 xx 4/5`

= `8/50`

D’s new share = `1/10 xx 4/5`

= `4/50`

E’s share is `1/5`. To compare it with the other shares, convert it to an equivalent fraction with a denominator of 50:

E’s share = `1/5`

= `(1 xx 10)/(5 xx 10)`

= `10/50`

The new shares for A, B, C, D, and E `12/50 : 16/50 : 8/50 : 4/50 : 10/50` or 12 : 16 : 8 : 4 : 10 or 6 : 8 : 4 : 2 : 5.