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.Options8:8:89:9:104:7:99:8:76:5:4
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.Options8:8:89:9:104:7:99:8:76:5:4
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
Substituting the given values, we get:
2 = 4 * Time_P 3 = 6 * Time_Q 5 = 9 * Time_R
Solving these equations for Time_P, Time_Q, and Time_R, we get:
Time_P = 2/4 = 0.5 Time_Q = 3/6 = 0.5 Time_R = 5/9 = 0.555...
So, the ratio of time for which they invested their capitals is 0.5:0.5:0.555..., which simplifies to 9:9:10.
Therefore, the correct answer is 9:9:10.
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