X and y are partners sharing profits 75 paise and 25paise in a rupee. Z is admitted as a partner. They decided to share profits in following ratio in future :x4, y:3, z:2:reserves 1 find out sacrifice Or gain of old partners.?

Question

Answer

Calculation of New Profit Sharing Ratio

X's new ratio = 4/9

Y's new ratio = 3/9 = 1/3

Z's new ratio = 2/9

Calculation of Sacrifice or Gain of Old Partners

Old Ratio of X = 75/100 = 3/4

Old Ratio of Y = 25/100 = 1/4

Combined Old Ratio of X and Y = 3/4 + 1/4 = 1

Calculation of Sacrifice or Gain of X

X's new share = 4/9

X's sacrifice = Old share - New share

X's sacrifice = (3/4) - (4/9)

X's sacrifice = 3/36 = 1/12

X's sacrifice = (1/12) x Total Profit

Calculation of Sacrifice or Gain of Y

Y's new share = 1/3

Y's sacrifice = Old share - New share

Y's sacrifice = (1/4) - (1/3)

Y's sacrifice = -1/12

Y's gain = (1/12) x Total Profit

Calculation of Sacrifice or Gain of Z

Z's new share = 2/9

Z's capital = (2/9) x Total Capital

Calculation of Reserves

Reserves = (Total Profit - X's sacrifice + Y's gain) x 1/10

Explanation
The new profit sharing ratio of X, Y, and Z is 4:3:2. This means that X will receive a higher share of profits, Y will receive a lower share, and Z will receive a moderate share. To calculate the sacrifice or gain of old partners, we first need to calculate their old ratio. X's old ratio is 3/4 and Y's old ratio is 1/4. The combined old ratio of X and Y is 1. This means that the total profit was divided between X and Y in the ratio of 3:1.

To calculate X's sacrifice, we subtract his new share from his old share. X's sacrifice is 1/12 of the total profit. This means that he will receive 1/12 less profit than he did before. Y's gain is also 1/12 of the total profit, as she will receive a higher share of profits under the new ratio. Z's capital is 2/9 of the total capital, which means that he will invest this amount in the business.

Finally, we calculate the reserves, which are set aside for future use. The reserves are calculated as 1/10 of the total profit minus X's sacrifice plus Y's gain. The reserves can be used to cover losses or to invest in the business

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