**Concept:** The question tests on the basics of Ratios(Partnerships)

**Solution:**

Ratio of which profits are shared depends on the investments made and the time period for which they they are made.

In effect Pa : Pb : Pc = Ia x ta : Ib x tb : Ic x tc, where t is in months.

Ia = 5600, ta = 3 months, Is = 3400, ts = 5 months, Ik = 8100 and tk = 2 months

Therefore Pa : Ps : Pk = (5600 * 3) : (3400 * 5) : (8100 * 2) = 84 : 85 : 81

Let the profit shares be 84x, 85x and 81x

Then 84x + 85x + 81x = 1500

250x = 1500

x = 6

The shares are 6 * 84 = 504, 6 * 85 = 510 and 6 * 81 = 486

**Option C**