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?

Correct Answer: (A) ₹ 12,000

Let total capital be 12 units and total duration be 12 units. A invests $\frac{1}{3}\times 12=4$$\frac{1}{3}$ $\times$ 12 = 4 capital for $\frac{1}{3}\times 12=4$$\frac{1}{3}$ $\times$ 12 = 4 time, giving an effective investment of $4$$\times$ 4 = 16. B invests $\frac{1}{4}\times 12=3$$\frac{1}{4}$ $\times$ 12 = 3 capital for $\frac{1}{4}\times 12=3$$\frac{1}{4}$ $\times$ 12 = 3 time, giving an effective investment of $3$$\times$ 3 = 9. C invests the remaining capital $12 - (4 + 3) = 5$ for the full duration of 12, giving an effective investment of $5$$\times$ 12 = 60. The profit-sharing ratio is $A : B : C = 16 : 9 : 60$, with total ratio parts $16 + 9 + 60 = 85$. Out of ₹ 17,000 profit, C receives $\frac{60}{85}\times 17,000=60\times 200=\text{₹ }12,000$$\frac{60}{85}$ $\times$ 17,000 = 60 $\times$ 200 = $\text{₹ }$ 12,000.