Question

X and Y are partners sharing profits in the ratio 5 : 3. They admitted Z for `1/5`th profits, for which he paid ₹ 60,000 against capital and ₹ 30,000 against goodwill. Find the capital balance for each partner, taking Z’s capital as base capital.

Options

• ₹ 1,50,000, ₹ 60,000 and ₹ 60,000

• ₹ 1,50,000, ₹ 60,000 and ₹ 90,000

• ₹ 1,50,000, ₹ 90,000 and ₹ 60,000

• ₹ 1,50,000, ₹ 90,000 and ₹ 90,000

Answer 1

₹ 1,50,000, ₹ 90,000 and ₹ 60,000

Explanation:

Z’s Share = `1/5`

X + Y Share = `1 - 1/5`

= `4/5`

X’s New Share = `4/5 xx 5/8`

= `20/40`

= `1/2`

Y’s New Share = `4/5 xx 3/8`

= `12/40`

= `3/10`

New ratio of X, Y, and Z = `1/2 : 3/10 : 1/5`

To simplify, use a common denominator of 10:

X’s New Share = `1/2`

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

= `5/10`

Y’s New Share = `3/10`

Z’s New Share = `1/5`

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

= `2/10`

New ratio of X, Y, and Z = `5/10 : 3/10 : 2/10` or 5 : 3 : 2

Total capital = 60,000 × 5

= 3,00,000

X’s capital = `3,00,000 xx 5/10`

= 1,50,000

Y’s capital = `3,00,000 xx 3/10`

= 90,000

Z’s capital = `3,00,000 xx 2/10`

= 60,000