Multiple choice

X & Y sharing profits & losses in the ratio of $5:3$ respectively. They tookk Z for $1/5$th share of profits Z was to pay Rs.$50,000$ as capital and Rs.$16,000$ for his share of goodwill. Capital accounts of the old partner were to be adjusted in the new profit sharing ratio taking Z's capital as base. Capital of X,Y & Z will be ____________________.

  1. $1,00,000:67,500:50,000$
  2. $1,50,000:87,500:50,000$
  3. $1,20,000:76,000:60,000$
  4. $1,25,000:75,000:50,000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

New profit sharing ratio: Z gets 1/5. Remaining 4/5 shared by X and Y in 5:3. X = 5/8 * 4/5 = 1/2. Y = 3/8 * 4/5 = 3/10. New ratio = 1/2 : 3/10 : 1/5 = 5:3:2. Total capital based on Z's 50,000 for 1/5 share = 250,000. X = 5/10 * 250,000 = 125,000. Y = 3/10 * 250,000 = 75,000. Z = 50,000.

AI explanation

Since Z acquires a 1/5th share in the new firm, the combined capital of the firm based on Z's Rs. 50,000 capital is Rs. 50,000 multiplied by 5, yielding Rs. 2,50,000. The remaining partners X and Y share the remaining 4/5th of the profits, and their old ratio of 5:3 is equivalent to a new ratio of 25:15, or 5:3 relative to each other. Their required capitals are calculated by taking 4/5 of Rs. 2,50,000, resulting in Rs. 2,00,000, which is then distributed in their new ratio. This makes X's capital Rs. 1,25,000 and Y's capital Rs. 75,000, resulting in the capitals of X, Y, and Z being Rs. 1,25,000, Rs. 75,000, and Rs. 50,000 respectively.

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