Correct Answer - Option 4 : 20 months

**Given:**

Initial investments' ratio of A and B = 4: 5

Ratio of their annual profits = 3: 5

**Calculation**

Let us assume that

A invests 4x amount for 10 months and

B invests 5x amount for y months

According to the question,

(4x × 10)/(5x × y) = 2/5

20x × 10 = 10xy

Y = 20 months

Hence, B invested for 20 months