rrect 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?Options34 : 14 : 5035 : 50 : 1435 : 14 : 5014 : 35 : 50
Question
rrect 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?Options34 : 14 : 5035 : 50 : 1435 : 14 : 5014 : 35 : 50
Solution
The ratio of their investments is 6:5:7 and the ratio of their profits is 3:1:5.
The profit of an investment is directly proportional to the product of the money invested and the time for which it is invested. Therefore, the ratio of the time for which they invested can be calculated as follows:
Let's denote the time for which P, Q, and R invested as Tp, Tq, and Tr respectively.
According to the problem,
6Tp : 5Tq : 7*Tr = 3 : 1 : 5
By simplifying this, we get the ratios of Tp, Tq, and Tr as follows:
Tp : Tq : Tr = (3/6) : (1/5) : (5/7) = 1/2 : 1/5 : 5/7
To make it easier to compare, we can find the least common multiple of the denominators 2, 5, and 7, which is 70. Multiply each ratio by 70 to get rid of the fractions:
Tp : Tq : Tr = 35 : 14 : 50
So, the ratio of the time in which they invested in the business is 35:14:50.
Similar Questions
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