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Select the correct answerP, Q and R start a business with investments of Rs. 90000, Rs. 60000 and Rs. 45000 respectively.PA and Q leave the business after a few months at the same time. At the end of the year, they share the profits in the ratio of 6 : 4 : 9. After how many months did P and Q leaves the business?Options3 months6 months9 months4 months

Question

Select the correct answerP, Q and R start a business with investments of Rs. 90000, Rs. 60000 and Rs. 45000 respectively.PA and Q leave the business after a few months at the same time. At the end of the year, they share the profits in the ratio of 6 : 4 : 9. After how many months did P and Q leaves the business?Options3 months6 months9 months4 months

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Solution

To solve this problem, we need to understand that the profit shared is directly proportional to the investment and the time duration of the investment.

Let's denote the time duration of investment for P, Q, and R as Tp, Tq, and Tr respectively. Given that P and Q leave the business at the same time, we can say that Tp = Tq.

The profit ratio is given as 6:4:9. We can write this in terms of investment and time duration as:

90000Tp : 60000Tq : 45000*12 = 6 : 4 : 9

Simplifying this, we get:

2Tp : 2Tq : 9 = 6 : 4 : 9

Tp : Tq : 4.5 = 6 : 4 : 9

From this, we can see that Tp = Tq = 6 months.

So, P and Q left the business after 6 months.

This problem has been solved

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