Question

X,Y,Z are partner sharing profit and lossees in the ration of 5:3:2 they admit A into partnership and give him 1/5th share of profits . Find the new profit -sharing ration​

Answer 1

Explanation:

Solution :

★ Old Ratio :

X : Y : Z = 5 : 3 : 2

• X's Share = 5/10
• Y's Share = 3/10
• Z's Share = 2/10

They admit A into partnership and give him 1/5th share of profits.

• A's Share = 1/5

Let,

Total Profit of all Partners = 1

• A's Share = 1/5

So,

Remaining Share = 1 - 1/5 = 4/5

★ New Profit Sharing Ratio :

• X's New Share =

⇒ 5/10 × 4/5 = 20/50

• Y's New Share =

⇒ 3/10 × 4/5 = 12/50

• Z's New Share =

⇒ 2/10 × 4/5 = 8/50

• A's Share =

⇒ 1/5 = (1×10)/(5×10)

⇒ 10/50

New Profit Sharing Ratio =

• X : Y : Z : A
• 20/50 : 12/50 : 8/50 : 10/50

⇒ 20 : 12 : 8 : 10 = 10 : 6 : 4 : 5

Therefore,

New Profit Sharing Ratio =

X : Y : Z : A = 10 : 6 : 4 : 5

Answer 2

Information provided with us:

• Ratio in which X , Y and Z are sharing profit and losses is 5:3:2.
• A is admitted into partnership
• He has been given 1/5th share of profit

What we have to calculate:

• New profit-sharing ratio

According to the question:

• Old profit and losses ratio is 5:3:2

X , Y and Z shares would be,

➟ X share = 5 / 5+3+2

➟ X share = 5/10

Share of Y,

➟ Y share = 3 / 5+3+2

➟ Y share = 3/10

Share of Z,

➟ Z share = 2 / 5+3+2

➟ Z share = 2/10

Given:-

• A is admitted into partnership and 1/5th shares of profit.

So, share of A would be, 1/5

Assuming that,

• Total share as 1.

Therefore, share of A would be 1/5

______________

Finding out remaining shares,

• In order to find out the remaining shares we would the total share that is 1 with A's share that is 1/5

➨ Remaining share = 1 - 1/5

➨ Remaining share = 5-1/5

➨ Remaining share = 4/5

Finding out new shares:

• In order to calculate the new profit sharing ratio we would multiply the shares of each X , Y and Z with remaining share that is 4/5

New share of X,

➨ New share of X = 5/10 × 4/5

➨ New share of X = 20 / 50

New share of Y

➨ New share of Y = 3/10 × 4/5

➨ New share of Y = 12/50

New share of A,

➨ New share of A = 1/5 × 10/10

➨ New share of A = 10/50

• Now we got the new profit sharing ratio of X , Y , Z and A respectively. So at last we would be calculating the new profit sharing ratio.

Finding out new profit sharing ratio:

➨ New profit sharing ratio = X : Y : Z : A

• Substituting the values,

➨ New profit sharing ratio = 20/50 : 12/50 : 8/50 : 10/50

• 50 would be cancelled off from each of that fraction.

➨ New profit sharing ratio = 20 : 12 : 8 : 10

• Reducing them (i.e., simplifying them)

➨ New profit sharing ratio = 10 : 6 : 4 : 5

Conclusion:

• New profit sharing ratio is 10 : 6 : 4 : 5