Question

X and Y are partners sharing profits in the ratio of 4 : 3. Z is admitted for a `1/5`th share and he brings in ₹ 1,40,000 as his share of goodwill in cash, of which ₹ 1,20,000 is credited to X and the remaining amount to Y. New profit sharing ratio will be ______.

Options

• 4 : 3 : 5

• 2 : 2 : 1

• 1 : 2 : 2

• 2 : 1 : 2

Answer 1

X and Y are partners sharing profits in the ratio of 4 : 3. Z is admitted for a `1/5`th share and he brings in ₹ 1,40,000 as his share of goodwill in cash, of which ₹ 1,20,000 is credited to X and the remaining amount to Y. New profit sharing ratio will be 2 : 2 : 1.

Explanation:

X = 1,20,000

Y = 20,000

Calculate Sacrificed Ratio:

Sacrificing Ratio = 6 : 1

Z = `1/5`

X’s Sacrificed Share = `6/7 xx 1/5`

= `6/35`

Y’s Sacrificed Share = `1/7 xx 1/5`

= `1/35`

Calculate the New Profit-Sharing Ratio

X’s New Share = `4/7 - 6/35`

= `(4 xx 5)/(7 xx 5) - 6/35`

= `20/35 - 6/35`

= `14/35`

Y’s New Share = `3/7 - 1/35`

= `(3 xx 5)/(7 xx 5) - 1/35`

= `15/35 - 1/35`

= `14/35`

Z’s New Share = `1/5`

= `(1 xx 7)/(5 xx 7)`

= `7/35`

The new ratio of X, Y, and Z = `14/35 : 14/35 : 7/35` or 14 : 14 : 7 or 2 : 2 : 1.