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.
Since Q joins after n months, the number of months he is in business = 12 - n
Therefore 2 : 1 = 7200 * 12 : 5400 * (12 - n) i.e 21=7200 ∗ 125400 ∗ (12−n)21=7200 ∗ 125400 ∗ (12−n)
2 * 54 * (12 - n) = 72 * 12
12 - n = 8
n = 4 months
Option C