Amit and Brijesh started a business with initial investments in the ratio of 12 : 11 and their annual profits were in the ratio of 4 : 1. If Amit invested the money for 11 months, then for what time Brijesh invested the money?

Let investment of Amit = 12k
and investment of Brijesh = 11k
Let Brijesh invested the money for N months.
Then,
Amit's investment : Brijesh's investment
= (12k x 11) : (11k x N) = 132k : 11kN = 12 : N
∴ 12/N = 4/1 [ ∵ ratio of profit is 4 : 1]
⇒ 4N = 12
∴ N = 12/4 = 3 months
Clearly, Brijesh invested money for 3 months.