Question

0.7. P, Q and R are in partnership sharing profits and losses as 1/2, 2/6 and 1/6
respectively. R retires and his share is taken by P and Q in the ratio of 2 : 1.
Immediately, S is admitted for 1/4th share of profit, 1/3rd of which was given by P and
the remaining share was taken equally from P and Q. Calculate new profit-sharing
ratio after S's admission.
[Ans. New Profit Sharing Ratio of P, Q and S = 16:11:9.]
? Tind out​

Answer 1

Solution :-

→ Old ratio (P, Q and R) = 1/2 : 2/6 : 1/6 = 3 : 2 : 1

→ New Ratio (P and Q) = 2 : 1

• Gaining ratio = New ratio - Old ratio

So,

→ P's gain = (2/3) - (3/6) = (4 - 3)/6 = 1/6

→ Q's gain = (1/3) - (2/6) = 0

On S's admission :-

→ Old ratio (P and Q) = 2 : 1

Now, we have given that, S is admitted for 1/4 shares and,

→ P's sacrifice in favour of S = (1/4) * (3/4) = 3/16

→ Q's sacrifice in favour of S = (1/4) * (1/4) = 1/16

therefore,

• New ratio = Old ratio - sacrificing ratio

→ P's new share = (2/3) - (3/16) = (32-9)/48 = (23/48)

→ Q's new share = (1/3) - (1/16) = (16-3)/48 = (13/48)

→ S's share = P's sacrifice + R's sacrifice

= (3/16) + (1/16)

= (1/4)

Hence,

→ New ratio of P, Q and S is = (23/48) : (13/48) : (1/4) = 23 : 13 : 12 .

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Answer 2

Full answer is in the pics and it is correct answer.