Three partners invested in a business in the ratio 6:3:2. They invested their capitals for 7 months, 4 months and 3 months,respectively. What was the ratio of their profits?

Correct option is B

Given:

Capital ratio of partners = 6:3:2

Time periods for which they invested = 7 months, 4 months, and 3 months respectively.

Concept Used:

The profit ratio is directly proportional to the capital invested and the time period of investment.

Profit Ratio = Capital Ratio × Time Period Ratio

Solution:

Let the capitals invested by the partners be 6x, 3x, and 2x respectively.

The time periods are 7 months, 4 months, and 3 months respectively.

Now, the profit ratio will be:

Profit Ratio = (6x × 7) : (3x × 4) : (2x × 3)

Simplifying the expression:

Profit Ratio = 42x : 12x : 6x

Now, cancel out the common factor 'x' from all terms:

Profit Ratio = 42 : 12 : 6

Finally, divide by the greatest common divisor, which is 6:

Profit Ratio = 7 : 2 : 1

Thus, the ratio of their profits is 7:2:1.