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

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Solution

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

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