Question

X, Y and Z are partners sharing profits and losses in the ratio of 5 : 3 : 2 . They admit A into partnership and give him 1/5th share of profits. Find the new profit-sharing ratio.

Answer 1

Answer:

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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

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: $10:6:4:5$

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