Select the correct answerP, 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.Options9:8:78:8:84:7:99:9:106:5:4
Question
Select the correct answerP, 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.Options9:8:78:8:84:7:99:9:106:5:4
Solution
The problem is about the relationship between the amount of capital invested, the time of investment, and the profit received.
The formula for profit in a business involving multiple partners is:
Profit = Capital * Time
Given that the ratio of capitals P, Q, and R invested is 4:6:9 and the ratio of their profits is 2:3:5, we can write the equation for each person as:
Profit_P = Capital_P * Time_P Profit_Q = Capital_Q * Time_Q Profit_R = Capital_R * Time_R
We can substitute the given ratios into these 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...
To find the ratio of time for which they invested their capitals, we need to express these times in the same terms. Multiplying each by 18 (the least common multiple of 4, 6, and 9) gives us:
Time_P = 0.5 * 18 = 9 Time_Q = 0.5 * 18 = 9 Time_R = 0.555... * 18 = 10
So, the ratio of time for which they invested their capitals is 9:9:10. Therefore, the correct answer is 9:9:10.
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