Question

X and Y are partners sharing profit in the ratio of 3 : 2. Z was admitted with 1/4 share in profits
which he acquires equally from X and Y. The new ratio will be:
a) 9 : 6 : 5
b) 19 : 11 : 10
c) 3 : 3 : 2
d) 3 : 2 : 4

Answer 1

Given:

• X and Y are partners in a firm, sharing profits and losses in the ratio 3:2.
• Z was admitted into the firm for 1/4th share in profits, which he acquires equally from X and Y.

To find: The new profit-sharing ratio.

Answer:

• X's old share = 3/5
• Y's old share = 2/5

• Z's share = 1/4

Since Z acquires 1/4 from X and Y equally, half of 1/4, i.e., 1/4 ÷ 2 = 1/8 will be deducted from X's and Y's share.

Calculation of the new profit-sharing ratio:

New share = Old share - Sacrifice to be made

For X:

• New share = 3/5 - 1/8 = (24 - 5)/40 = 19/40

For Y:

• New share = 2/5 - 1/8 = (16 - 5)/40 = 11/40

For Z:

• New share = 1/4, or 10/40

Therefore, the new profit-sharing ratio is (B) 19:11:10.