In a partnership, A invests one-fourth of the capital for one-third of the time, B invests one-third of the capital for one-fourth of the time and C invests the rest of the capital for the whole time. Out of a profit of ₹3,500, A’s share is:

₹500

The correct answer is Option (3) - ₹500

$\text{Let total capital} = 1,\;\; \text{total time} = 1$

$\text{A: } \frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$

$\text{B: } \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$

$\text{C: } 1 - \left(\frac{1}{4} + \frac{1}{3}\right) = \frac{5}{12},\;\; \text{time} = 1$

$\text{C: } \frac{5}{12} \times 1 = \frac{5}{12}$

$\text{Ratio} = \frac{1}{12} : \frac{1}{12} : \frac{5}{12} = 1 : 1 : 5$

$\text{Total parts} = 7$

$\text{A’s share} = \frac{1}{7} \times 3500 = 500$

A’s share is ₹500.