A starts a flower shop with an investment Tk. 8000. After 3 months B joins him with an investment of Tk. 16000. C joins them later with an investment of Tk. 40,000/-. The business prospers and makes a profit of Tk. 1,12,000/- at the end of the year. If profits of A, B and C are in the ratio of 6 : 9 : 5, for how many months was C a part of the business?

We know that
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment × Time) : (B's investment × Time) = Profit of A : Profit of B

∴ Tk. 8000 × 12 months : Tk. 16000 × 9 months : Tk. 40000 × ? months = 6 : 9 : 5
∴ 96000 : 144000 : 40000 × ? = 6 : 9 : 5
By direct observation we can say, if common factor is K, then
6K = 96000;
∴ K = 16000;
and 5K = 40000 × ?
? = 5k/40000
= (5 × 16000)/40000
= 2 months.