Question

P, Q, R and S were partners sharing profits in the ratio of 2:3:5:2.S retires and his share is acquired by Q and R in the ratio of 3 : 2. Calculate new ratio
and gaining ratio.

Answer 1

Explanation:

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Answer 2

Given:

• P, Q, R and S were partners in a firm, sharing profits and losses in the ratio 2:3:5:2.
• S retired.
• S's share is taken by Q and R in the ratio 3:2.

To find: The new profit-sharing ratio and the gaining ratio.

Answer:

• P's old share = 2/12
• Q's old share = 3/12
• R's old share = 5/12
• S's old share = 2/12

S's share, i.e., 2/12, is to be taken by Q and R in the ratio 3:2.

From S, Q gets:

• 2/12 × 3/5 = 6/60

From S, R gets:

• 2/12 × 2/5 = 4/60

Calculation of the new profit-sharing ratio:

New ratio = Old ratio + Gain from the retiring partner

P's share remains the same.

For P:

• New ratio = 2/12, or 10/60

For Q:

• New ratio = 3/12 + 6/60 = (15 + 6)/60 = 21/60

For R:

• New ratio = 5/12 + 4/60 = (25 + 4)/60 = 29/60

Therefore, the new profit-sharing ratio is 10:21:29.

Calculation of the gaining ratio:

Gain = New ratio - Old ratio

For P:

• Gain = 10/60 - 2/12 = (10 - 10)/60 = 0

For Q:

• Gain = 21/60 - 3/12 = (21 - 15)/60 = 6/60

For R:

• Gain = 29/60 - 5/12 = (29 - 25)/60 = 4/60

Therefore, the gaining ratio is 0:6:4, or 0:3:2.

Even without the calculations, we can consider the gaining ratio to be 0:3:2, since the ratio in which the continuing partners gain from the retiring partner is given.