-    David : Robert : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24)
  = 12 : 15: 16

Let's assume the amount of profit earned by the business is X.

David invested Rs. 70,000 for a period of 3 years, which is equivalent to (3 * 12) 36 months.

Robert invested Rs. 1,05,000 for a period of 2.5 years, which is equivalent to (2.5 * 12) 30 months.

Sagar invested Rs. 1.4 lakhs for a period of 2 years, which is equivalent to (2 * 12) 24 months.

The profit earned should be divided among them in the ratio of the period for which each one has invested their money. Hence, the ratio is:

36 : 30 : 24 = 12 : 10 : 8

Now, we need to extend this ratio to include equal parts. The LCM of 12, 10 and 8 is 120, so the ratio becomes:

(12/120) : (10/120) : (8/120) = 12 : 10 : 8

Dividing each part by the same number, we get the final ratio:

12 : 15 : 16

To summarize:

• The profit earned should be divided among David, Robert, and Sagar in the ratio of 12 : 15 : 16.

Answer: B - 12:15:16.