X and Y partners in a firm sharing profits in the ratio 5 : 3. They admitted Z
as a new partner. The new profit sharing ratio will be 4 : 3 : 2. The firm’s
goodwill on Z’s admission was valued at Rs. 1,26,000. But Z could not bring
any amount of goodwill in cash. Credit will be given to :
a) X Rs. 17,500 ; and Y Rs. 10,500 b) X Rs. 22,750 ; and Y Rs. 5,250
Answers
Answer:
Answer is (b) X Rs. 22,750 and Y Rs. 5,250.
Explanation:
The change in the profit sharing ratio due to the admission of Z can be expressed as follows:
Let the original total profit be P.
Then, X's share = (5/8)P and Y's share = (3/8)P.
After Z's admission, the new total profit is divided in the ratio 4:3:2 between X, Y, and Z.
Let the new total profit be Q.
Then, X's share = (4/9)Q,
Y's share = (3/9)Q,
and Z's share = (2/9)Q.
The increase in X's share due to Z's admission is equal to the value of goodwill, which is Rs. 1,26,000.
So,we have:
Increase in X's share = X's share in the new profit sharing ratio - X's share in the original profit sharing ratio
= (4/9)Q - (5/8)P
= Rs. 1,26,000
Similarly, the increase in Y's share due to Z's admission is:
Increase in Y's share = Y's share in the new profit sharing ratio - Y's share in the original profit sharing ratio
= (3/9)Q - (3/8)P
We are not given the values of P and Q, but we can use the fact that X's and Y's shares add up to 8/8 in both the original and the new profit sharing ratios. That is:
(5/8)P + (3/8)P = P
(4/9)Q + (3/9)Q + (2/9)Q = Q
Simplifying these equations, we get:
P = (40/8)X
Q = (18/9)(X+Y+Z) = 2(X+Y+Z)
Substituting these values in the expressions for the increase in X's and Y's shares, we get:
(4/9)(2(X+Y+Z)) - (5/8)(40/8)X = 1,26,000
(3/9)(2(X+Y+Z)) - (3/8)(40/8)Y = 0
Simplifying these equations and solving for X and Y, we get:
X = Rs. 22,750
Y = Rs. 5,250
Therefore, the credit to X and Y will be Rs. 22,750 and Rs. 5,250, respectively, which is option (b).
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