Question

X and Y are partners sharing profits and losses in the ratio of 3 : 2. They admit Z into partnership, Z paying a premium of ₹ 2,00,000 for 1/4 share of the profits while X and Y as between themselves sharing profits and losses equally. Goodwill credited to X will be ______.

Options

• ₹ 1,20,000

• ₹ 1,80,000

• ₹ 1,00,000

• ₹ 20,000

Answer 1

X and Y are partners sharing profits and losses in the ratio of 3 : 2. They admit Z into partnership, Z paying a premium of ₹ 2,00,000 for 1/4 share of the profits while X and Y as between themselves sharing profits and losses equally. Goodwill credited to X will be ₹ 1,80,000.

Explanation:

Z’s share = `1/4`

Remaining share = `1 - 1/4`

= `3/4`

X’s new share = `3/4 xx 1/2`

= `3/8`

Y’s new share = `3/4 xx 1/2`

= `3/8`

Sacrifice by X = `3/5 - 3/8`

= `(3 xx 8)/(5 xx 8) - (3 xx 5)/(8 xx 5)`

= `24/40 - 15/40`

= `9/40`

Sacrifice by Y = `2/5 - 3/8`

= `(2 xx 8)/(5 xx 8) - (3 xx 5)/(8 xx 5)`

= `16/40 - 15/40`

= `1/40`

Sacrifice Ratio of X and Y = `9/40 : 1/40` or 9 : 1

X’s share of goodwill = `2,00,000 xx 9/10`

= 1,80,000