Question

Atul, Beena and Sita were partners in a firm sharing profits and losses in the ratio of 8 : 7 : 5. Damini was admitted as a new partner for the `1/5` th share in the profits, which she acquired entirely from Atul. The new profit-sharing ratio after Damini’s admission will be ______.

Options

• 7 : 7 : 5 : 1

• 4 : 7 : 5 : 4

• 8 : 7 : 5 : 4

• 7 : 5 : 8 : 4

Answer 1

Atul, Beena and Sita were partners in a firm sharing profits and losses in the ratio of 8 : 7 : 5. Damini was admitted as a new partner for the `1/5` th share in the profits, which she acquired entirely from Atul. The new profit-sharing ratio after Damini’s admission will be 4 : 7 : 5 : 4.

Explanation:

Atul, Beena, and Sita share profits in the ratio of 8 : 7 : 5. The sum of their ratios is 20.

Their initial shares are `8/20, 7/20, 5/20` respectively. Damini is admitted for a `1/5` share.

Damini acquires her entire `1/5` share, which is equivalent to `4/20` from Atul.

Atul’s new share = Atul’s original share − Share given to Damini

= `8/20 - 4/20`

= `4/20`

Beena and Sita make no sacrifice, so their shares remain unchanged at `7/20` and `5/20` respectively. Damini’s share is `4/20`.

The resulting shares for Atul, Beena, Sita, and Damini  = `4/20,  7/20, 5/20, and 4/20` or 4 : 7 : 5 : 4.