A starts a business with ₹ 4000. B joins him after 3 months with ₹ 8000. C puts a sum of ₹ 20000 in the business for 2 months only. At the end of year, the business gives a profit of ₹ 16800. How should the profit be divided amongst them?

A's share : B's share : C's share
= Ratio of product of investment and time period of investment
= 4000 x 12 : 8000 x (12 - 3) : 20000 x 2
= 4 x 12 : 8 x 9 : 20 x 2
= 6 : 9 : 5
Let,
A's share = 6N
B's share = 9N
C's share = 5N
According to the question,
6N + 9N + 5N = 16800
⇒ 20N = 16800
∴ N = 16800/20 = 840
∴ A's share = 6N = 6 x 840 = ₹ 5040
B's share = 9N = 9 x 840 = ₹ 7560
C's share = 5N = 5 x 840 = ₹ 4200