Kim and Sim are partners in a firm sharing profits in 4:3 ratio. They admitted Pim as a new partner for 1/4 share in the profits, which he acquired in the ratio of 3:2 from Kim and Sim. Determine the new profit sharing ratio of the partners.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 59:46:35
When the new partner takes his share from the old partners in a given ratio, each old partner’s new share = old share − share given up.
Share given up by each old partner (Pim’s 1/4 in 3:2):
Kim gives 1/4 × 3/5 = 3/20
Sim gives 1/4 × 2/5 = 2/20
New shares (LCM 140):
Kim = 4/7 − 3/20 = 80/140 − 21/140 = 59/140
Sim = 3/7 − 2/20 = 60/140 − 14/140 = 46/140
Pim = 1/4 = 35/140
New ratio = 59:46:35
In the NCERT illustration below the new partner takes his whole share from one partner; here he takes it from both in 3:2, so each old partner’s sacrifice is worked out first.
NCERT (2026-27 edition):
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