X and Y are partners in a firm sharing profits in the ratio of 4:3. They admitted Z as a new partner. The profit sharing ratio of X, Y and Z will be 2:3:1. Calculate the gain or sacrifice of Y.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Gain of 3/42 share in profit
A partner's gain or sacrifice is new share − old share. A positive answer is a gain, a negative one a sacrifice. Take both shares to a common denominator first.
Y's old share = 3/7 = 18/42
Y's new share = 3/6 = 21/42
Change = 21/42 − 18/42 = +3/42, a gain
Y gains even though a new partner has come in, because X gives up more than Z takes:
X's old share = 4/7 = 24/42
X's new share = 2/6 = 14/42
X's sacrifice = 24/42 − 14/42 = 10/42
Of this, 7/42 (Z's share of 1/6) goes to Z and 3/42 to Y
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27 edition):
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