Three partners invested in a business in the ratio 5:1:9. They invested their capitals for 2 months, 9 months and 11 months respectively. What was the ratio of their profits?

Correct option is D

Given:
Investment ratio of the three partners = 5 : 1 : 9
Investment periods = 2 months, 9 months, and 11 months respectively
Concept Used:

$$\text{Profit ratio} = \text{Investment} \times \text{Time period}$$​​
Solution:

Let the investments of the three partners be 5x , x and 9x respectively.
The profit ratio is calculated as:
$$\text{Profit ratio} = \text{Investment} \times \text{Time period}$$​​
​$$\text{Profit ratio} = (5x \times 2) : (x \times 9) : (9x \times 11)$$​​
$$\text{Profit ratio} = 10x : 9x : 99x$$​​
$$\text{Profit ratio} = 10 : 9 : 99$$​
Thus, option (d) is right.