swerP, Q and R invested capitals in the ratio 4: 6: 9. At the end of the business term, they received the profits in the ratio 2: 3: 5. Find the ratio of time for which they invested their capitals.
Question
swerP, Q and R invested capitals in the ratio 4: 6: 9. At the end of the business term, they received the profits in the ratio 2: 3: 5. Find the ratio of time for which they invested their capitals.
Solution
The profit received by each person is directly proportional to the product of the capital invested and the time for which it is invested. This can be represented as:
Profit = Capital * Time
Given that the ratio of capitals is 4:6:9 and the ratio of profits is 2:3:5, we can set up the following equations:
2 = 4 * Time_P 3 = 6 * Time_Q 5 = 9 * Time_R
Solving these equations for Time_P, Time_Q, and Time_R gives us:
Time_P = 2/4 = 0.5 Time_Q = 3/6 = 0.5 Time_R = 5/9 = 0.555...
Therefore, the ratio of time for which they invested their capitals is 0.5:0.5:0.555..., which simplifies to 10:10:11.
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