Question

Hema and Tara were partners in a firm sharing profits and losses in the ratio of 2 : 3. They admited Ojas as a new partner. Hema surrendered `1/3`rd of her share and Tara surrendered `1/2` of her share in favour of Ojas. The new profit-sharing ratio of Hema, Tara and Ojas will be ______.

विकल्प

• 8 : 9 : 13

• 3 : 2 : 5

• 2 : 3 : 5

• 2 : 3 : 25

Answer 1

Hema and Tara were partners in a firm sharing profits and losses in the ratio of 2 : 3. They admited Ojas as a new partner. Hema surrendered `1/3`rd of her share and Tara surrendered `1/2` of her share in favour of Ojas. The new profit-sharing ratio of Hema, Tara and Ojas will be 8 : 9 : 13.

Explanation:

Calculate the sacrifice of each partner.

Hema and Tara’s old profit-sharing ratio is 2 : 3.

Hema’s sacrifice = `1/3 xx 2/5`

= `2/15`

= `(2 xx 2)/(15 xx 2)`

= `4/30`

Tara’s sacrifice = `1/2 xx 3/5`

= `3/10`

= `(3 xx 3)/(10 xx 3)`

= `9/30`

Calculate the new share of each partner.

Hema’s new share = `2/5 - 4/30`

= `(2 xx 6)/(5 xx 6) - 4/30`

= `12/30 - 4/30`

= `8/30`

Tara’s new share = `3/5 - 3/10`

= `(3 xx 6)/(5 xx 6) - 9/30`

= `18/30 - 9/30`

= `9/30`

Ojas’s share is the sum of the sacrifices made by Hema and Tara.

Ojas’s share = `4/30 + 9/30`

= `13/30`

The new profit-sharing ratio for Hema, Tara, and Ojas = `8/30 : 9/30 : 13/30` or 8 : 9 : 13.