Question

P, Q and R are partners sharing profits and losses in the ratio of 5 : 3 : 2. S is admitted as a new partner for `1/5`th share. P sacrifices `1/10` th from his share in favour of S and remaining sacrifice was made by Q and R in the ratio of 2 : 1. Calculate sacrificing ratio and new profit sharing ratio.

Answer 1

Calculation of Sacrificing Ratio:

S’s share = `1/5`, Out of which `1/10` is given by P.

Remammg share of S = `1/5 - 1/10`

= `(1 xx 2)/(5 xx 2) - 1/10`

= `2/10 - 1/10`

= `(2 - 1)/10`

= `1/10`

This `1/10` share is sacrificed by Q and R in the ratio of 2 : 1

Hence, Q’s Sacrifice = `1/10 xx 2/3`

= `2/30`

R’s Sacrifice = `1/10 xx 1/3`

= `1/30`

To find the sacrificing ratio, express all sacrifices with a common denominator 30

P’s Sacrifice = `1/10`

= `(1 xx 3)/(10 xx 3)`

= `3/30`

Q’s Sacrifice = `2/30`

R’s Sacrifice = `1/30`

Sacrifice Ratio of P, Q and R = `3/30 : 2/30 : 1/30` or 3 : 2 : 1

Calculation of New Ratio:

P = `5/10 - 3/30`

= `(5 xx 3)/(10 xx 3) - 3/30`

= `15/30 - 3/30`

= `(15 - 3)/30`

= `12/30`

Q = `3/10 - 2/30`

= `(3 xx 3)/(10 xx 3) - 2/30`

= `9/30 - 2/30`

= `(9 - 2)/30`

= `7/30`

R = `2/10 - 1/30`

= `(2 xx 3)/(10 xx 3) - 1/30`

= `6/30 - 1/30`

= `(6 - 1)/30`

= `5/30`

S = `1/5`

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

= `6/30`

New Ratio of P, Q, R and S = `12/30 : 7/30 : 5/30 : 6/30` or 12 : 7 : 5 : 6