Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹ 17,000, how much profit will C get?

(a) ₹ 12,000 ✓ UPSC's answer
(b) ₹ 10,000
(c) ₹ 12,500
(d) ₹ 10,750

Why the answer is (a)

• Let the total capital be C and the total duration be T.

• A's investment share is (1/3)C for (1/3)T, giving a ratio factor of (1/3) * (1/3) = 1/9.

• B's investment share is (1/4)C for (1/4)T, giving a ratio factor of (1/4) * (1/4) = 1/16.

• C's investment share is the remaining capital (1 - 1/3 - 1/4 = 5/12)C for the whole duration T, giving a ratio factor of 5/12.

• The profit sharing ratio is 1/9 : 1/16 : 5/12. Multiplying by the LCM of 9, 16, and 12 (which is 144) gives 16 : 9 : 60.

• C's share of the ₹17,000 profit is (60 / (16 + 9 + 60)) * 17,000 = (60 / 85) * 17,000 = 12,000.

Why the other options are wrong

(b) ₹ 10,000: ₹10,000 does not correspond to the calculated profit-sharing ratio of 16:9:60.
(c) ₹ 12,500: ₹12,500 is an incorrect calculation that does not align with the proportional investment factors.
(d) ₹ 10,750: ₹10,750 is an incorrect value that fails to account for the specific fractional durations and capital contributions.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.