Ranjana, Sadhna and Kamana are partners sharing profits in the ratio 2:3:4 Ranjana retires; Sadhna and Kamana decided to share profits in future in the ratio of 3:5. Calculate the Gaining Ratio of Sadhna and Kamana.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Gaining ratio of Sadhna and Kamana 3:13
The gaining ratio is the ratio in which the continuing partners take over the retiring partner’s share. Each partner’s gain is new share − old share.
Old shares (ratio 2:3:4, total 9):
Sadhna = 3/9
Kamana = 4/9
New shares (ratio 3:5, total 8):
Sadhna = 3/8
Kamana = 5/8
Gains:
Sadhna = 3/8 − 3/9 = 27/72 − 24/72 = 3/72
Kamana = 5/8 − 4/9 = 45/72 − 32/72 = 13/72
Gaining ratio = 3/72 : 13/72 = 3:13
Check: 3/72 + 13/72 = 16/72 = 2/9, which is Ranjana’s old share. The new ratio 3:5 is not the gaining ratio, because Sadhna and Kamana did not start from equal shares.
Note: NTA picked this question from an NCERT (2026-27) illustration and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27 edition):
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