P invested Rs. 4000 for one year. Q joined him with an investment of Rs. 6000 after few months. If at the end of one year the ratio of profits of P and Q is 4 : 3. then Q joined after how many months ?

6 months 

Formula :-

The ratio of profit sharing = Ratio of (Investment × Time)

Since P invested for 12 months, Q invested for x months .

Ratio of their profit = 4 : 3

\(\frac{ (4000 × 12)}{(6000 × x)}\) = \(\frac{4}{3}\) 

36 = 6x

x = 6

So , Q joined after 6 months .