Select the correct answerP, Q, R invested in the ratio of 6 : 5 : 7. After the end of business term they receive the profit in the ratio 3 : 1 : 5. Find the ratio of time in which they invested in the business?Options35 : 50 : 1435 : 14 : 5034 : 14 : 5014 : 35 : 50
Question
Select the correct answerP, Q, R invested in the ratio of 6 : 5 : 7. After the end of business term they receive the profit in the ratio 3 : 1 : 5. Find the ratio of time in which they invested in the business?Options35 : 50 : 1435 : 14 : 5034 : 14 : 5014 : 35 : 50
Solution
The profit received by each person is directly proportional to the product of the money invested and the time for which it was invested.
Let's denote the time for which P, Q, and R invested as Tp, Tq, and Tr respectively.
According to the problem,
P's share / Q's share / R's share = (P's investment * Tp) / (Q's investment * Tq) / (R's investment * Tr)
Substituting the given values, we get
3/1/5 = (6Tp) / (5Tq) / (7*Tr)
From this, we can derive the ratios of time for which they invested as follows:
Tp/Tq/Tr = (3/1/5) / (6/5/7) = 35/14/50
So, the correct answer is 35 : 14 : 50.
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