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 sacrificed `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. S brings his share of goodwill, ₹ 60,000 in Cash. R’s share of goodwill will be ______.

Options

• ₹ 20,000

• ₹ 30,000

• ₹ 10,000

• ₹ 6,000

Answer 1

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 sacrificed `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. S brings his share of goodwill, ₹ 60,000 in Cash. R’s share of goodwill will be ₹ 10,000.

Explanation:

Share of S = `1/5`

P’s Sacrifice = `1/10`

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

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

= `2/10 - 1/10`

= `1/10`

This share i.e., `1/10`, is to be sacrificed by Q and R in 2 : 1

Q’s Sacrifice = `1/10 xx 2/3`

= `2/30`

R’s Sacrifice = `1/10 xx 1/3`

= `1/30`

Sacrificing Ratio of P, Q, and R = `1/10 : 2/30 : 1/30`

To simplify, use a common denominator of 30:

P’s Sacrifice = `1/10`

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

= `3/30`

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

R’s Share of Goodwill = `60,000 xx 1/6`

= 10,000