Question

A and B are in partnership sharing profits and losses as 3 : 2. C is admitted for a `1/4`th share. Afterwards D enters for 20 paisa in the rupee. The new profit-sharing ratio after D’s admission will be ______.

विकल्प

• 9 : 6 : 5 : 5

• 6 : 9 : 5 : 5

• 3 : 2 : 4 : 5

• 3 : 2 : 5 : 5

Answer 1

A and B are in partnership sharing profits and losses as 3 : 2. C is admitted for a `1/4`th share. Afterwards D enters for 20 paisa in the rupee. The new profit-sharing ratio after D’s admission will be 9 : 6 : 5 : 5.

Explanation:

Old Ratio = A : B = 3 : 2
C’s admitted for `1/4` share of profit

Remaining share for A and B after C’s admission:

1 − C’s share = `1 - 1/4`

= `3/4`

A’s new share = `3/4 xx 3/5`

= `9/20`

B’s new share = `3/4 xx 2/5`

= `6/20`

C’s share = `1/4`

= `(1 xx 5)/(4 xx 5)`

= `5/20`

The profit-sharing ratio of A, B, and C is 9 : 6 : 5.

Calculate the New Profit-Sharing Ratio after D’s Admission:

D enters for “20 paisa in the rupee,” which is `20/100 "or" 1/5` of the total profit.

Remaining share after D’s admission:

1 − D’s share = `1 - 1/5`

= `4/5`

This remaining `4/5` share is distributed among A, B, and C in their existing ratio of 9 ∶ 6 ∶ 5.

Sum of this ratio = 9 + 6 + 5

= 20

A’s new share = `4/5 xx 9/20`

= `36/100`

B’s new share = `4/5 xx 6/20`

= `24/100`

C’s new share = `4/5 xx 5/20`

= `20/100`

D’s new share = `1/5`

= `(1 xx 20)/(5 xx 20)`

= `20/100`

The new shares for A, B, C, and D = `36/100 : 24/100 : 20/100 : 20/100` or 36 : 24 : 20 : 20 or 9 : 6 : 5 : 5