Three partners invested in a business in the ratio 7:2:5. They invested their capitals for 11 months, 7 months and 12 months,respectively. What was the ratio of their profits?

Correct option is D

Given:
Investment ratio of three partners = 7 : 2 : 5
Time periods for which they invested their capitals = 11 months, 7 months, and 12 months, respectively
Formula Used:
Profit Sharing Ratio: In a partnership, the profit is shared in the ratio of the product of the capital invested and the time period for which it was invested.
​$$\text{Profit Ratio} = (\text{Capital}_1 \times \text{Time}_1) : (\text{Capital}_2 \times \text{Time}_2) : (\text{Capital}_3 \times \text{Time}_3)$$​​
Solution:
Let the investments of the three partners be 7x ,2x and 5x  respectively.
Partner 1: 7x$$\times$$​ 11 = 77x 
Partner 2: 2x$$\times$$​ 7 = 14x 
Partner 3: 5x$$\times$$​ 12 = 60x 
Profit Ratio = 77x : 14x : 60x
Profit Ratio = 77 : 14 : 60 
Option (d) is right.