P and Q are partners sharing profits in the ratio of 2 : 1. They admitted R into partnership giving him 1/5th share which he acquired from P and Q in 1 : 2 ratio. Calculate the new profit sharing ratio.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 : 1 : 1
R takes 1/5 of the profits and gets it from P and Q in the ratio 1 : 2, so each old partner’s sacrifice is that part of 1/5, and his new share is his old share less the sacrifice.
P’s sacrifice = 1/5 × 1/3 = 1/15
Q’s sacrifice = 1/5 × 2/3 = 2/15
P’s new share = 2/3 − 1/15 = 10/15 − 1/15 = 9/15
Q’s new share = 1/3 − 2/15 = 5/15 − 2/15 = 3/15
R’s share = 1/5 = 3/15
New profit sharing ratio = 9 : 3 : 3 = 3 : 1 : 1
NCERT (2026-27 edition):
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