Question

Rekha, Sunita and Teena are partners in a firm sharing profits in the ratio of 3 : 2 : 1. Samiksha joins the firm. Rekha surrenders `1/4`th of her share; Sunita surrenders `1/3`rd of her share and Teena `1/5`th of her share in favour of Samiksha. Find the new profit-sharing ratio.

Answer 1

Calculate the share surrendered by partners:

Rekha’s surrendered share = `1/4 xx 3/6`

= `3/24`

Sunita’s surrendered share = `1/3 xx 2/6`

= `2/18`

Teena’s surrendered share = `1/5 xx 1/6`

= `1/30`

Calculate the new share of each old partner:

Rekha’s new share = `3/6 - 3/24`

= `(3 xx 4)/(6 xx 4) - 3/24`

= `12/24 - 3/24`

= `(12 - 3)/24`

= `9/24`

Sunita’s new share = `2/6 - 2/18`

= `(2 xx 3)/(6 xx 3) - 2/18`

= `6/18 - 2/18`

= `(6 - 2)/18`

= `4/18`

Teena’s new share = `1/6 - 1/30`

= `(1 xx 5)/(6 xx 5) - 1/30`

= `5/30 - 1/30`

= `(5 - 1)/30`

= `4/30`

Samiksha’s share is the sum of the shares surrendered by Rekha, Sunita, and Teena.

Samiksha’s share = `3/24 + 2/18 + 1/30`

The least common multiple of 24, 18, 30 is 360.

Samiksha’s share = `(3 xx 15)/(24 xx 15) + (2 xx 20)/(18 xx 20) + (1 xx 12)/(30 xx 12)`

= `45/360 + 40/360 + 12/360`

= `(45 + 40 + 12)/360`

= `97/360`

Calculate the new profit-sharing ratio:

To find the new ratio, express all the new shares with a common denominator of 360.

Rekha’s new share = `9/24`

= `(9 xx 15)/(24 xx 15)`

= `135/360`

Sunita’s new share = `4/18`

= `(4 xx 20)/(18 xx 20)`

= `80/360`

Teena’s new share = `4/18`

= `(4 xx 12)/(30 xx 12)`

= `48/360`

Samiksha’s share = `97/360`

The new profit-sharing ratio of Rekha, Sunita, Teena, and Samiksha = `135/360 : 80/360 : 48/360 : 97/360` or 135 : 80 : 48 : 97.