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UPSC Prelims 2026 CSAT, question 78

Topic: Arithmetic

Q78

Three partners A,BA,B and CC entered into a business. AA invested one-third of the capital for one-third duration. BB invested one-fourth of the capital for one-fourth duration. CC invested the remaining capital for the whole duration. Out of a profit of ₹ 17,00017,000, how much profit will CC get?

  1. (a) ₹ 12,000Correct answer
  2. (b) ₹ 10,000
  3. (c) ₹ 12,500
  4. (d) ₹ 10,750

Solution.

Answer: (a) ₹ 12,000

  1. The remaining capital invested by CC is 1−13−14=5121 - \frac{1}{3} - \frac{1}{4} = \frac{5}{12} for the full duration (11).
  2. The profit-sharing ratio A:B:CA : B : C is (13×13):(14×14):(512×1)=19:116:512=16:9:60(\frac{1}{3} \times \frac{1}{3}) : (\frac{1}{4} \times \frac{1}{4}) : (\frac{5}{12} \times 1) = \frac{1}{9} : \frac{1}{16} : \frac{5}{12} = 16 : 9 : 60 (multiplying by 144144).
  3. Out of a total profit of ₹17,00017,000, CC's share is 6016+9+60×17,000=6085×17,000=12,000\frac{60}{16 + 9 + 60} \times 17,000 = \frac{60}{85} \times 17,000 = 12,000 rupees.