A, B and C started a business They partnered for 6 months, 12 months, 14 months respectively, If their profit is in the ratio 5 : 4 : 7 respectively, then the ratio of their respective investments is ___________.

Correct option is A

Given:

The profit ratio of A, B, and C = 5 : 4 : 7
Their respective partnership durations:
- A's duration = 6 months
- B's duration = 12 months
- C's duration = 14 months

Formula Used:

$$Investment = \frac{\text{Profit}}{\text{Time}}$$​

1. Let the investments of A, B, and C be represented by their profits and partnership durations:

​$$- A's effective investment ratio = \frac{5}{6}$$​

​$$- B's effective investment ratio = \frac{4}{12}$$​

​$$- C's effective investment ratio = \frac{7}{14}$$​

2. Convert these into a common base to find the ratio of investments:

Simplifying each:
​$$- A's effective investment = \frac{5}{6}$$​
​$$- B's effective investment = \frac{4}{12} = \frac{1}{3}$$​
​$$- C's effective investment = \frac{7}{14} = \frac{1}{2}$$​

3. Find the LCM of the denominators (6, 3, and 2) to get a common base for comparison:

- LCM = 6

Converting each ratio to have a denominator of 6:
- A's investment ratio = 5
- B's investment ratio = 2
- C's investment ratio = 3

Answer: The ratio of their respective investments is 5 : 2 : 3.