Question

X Y and Z Are partners sharing profit and losses in the ratio 5:3:2 . They admitted A into partnerships and give him 1/5th share of profit . Find the new profit sharing ratio

Answer 1

Explanation:

X's old ratio= 5/10

Y's old ratio= 3/10

Z's old ratio= 2/10

A is admitted for 1/5th share in the profits.

Hence, remaining share= 1-[1/5]

= 4/5

New Profit sharing ratio:

X's new share= 5/10 * 4/5

= 2/5

Y's new share= 3/10 * 4/5

= 6/25

Z's new share= 2/10 * 4/5

= 4/25

A's new share= 1/5

New profit ratio= 10:6:4:5

Answer 2

Explanation:

New Profit ratio is

calculated below.

Explanation:

The given ratio of X:Y:Z is 5:3:2.

A is to be provided 1/5th share of Profits

Assuming combined share of profit for all partners after A's admission be =1

Accordingly, combined share of X, Y and Z after A's admission =1-A's share

After A’s admission, share for all three can be calculated as:

Combined share of X, Y, and Z

$=1-\frac{1}{5}=\frac{4}{5}=$

Calculation of New Ratio

New Ratio = Old Ratio * Combined share of X, Y and Z.

X’s share

$=\frac{5}{10} \times \frac{4}{5}=\frac{20}{50}=$

Y’s share

$=\frac{3}{10} \times \frac{4}{5}=\frac{12}{50}=$

Z’s share

$=\frac{2}{10} \times \frac{4}{5}=\frac{8}{50}$

Thus, new ratio of X, Y, Z and A is:

$\frac{20}{50}: \frac{12}{50}: \frac{8}{50}: \frac{1}{5}$

This can also be written as: 10:6:4:510:6:4:5

Thus, the new profit sharing ratio is 10 : 6 : 4 : 5