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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?Options6 months9 months3 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?Options6 months9 months3 months4 months

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Solution

The profit share at the end of the year is proportional to the product of the initial 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 the profit share ratio is 6:4:9, we can write the following equations:

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

Since P and Q leave the business at the same time, Tp = Tq. Let's denote this common time duration as T.

So, the equations become:

90000 * T : 60000 * T : 45000 * Tr = 6 : 4 : 9

Simplifying, we get:

T : T : 45000 * Tr = 6 : 4 : 9

This implies that Tr = 12 months (since R stayed for the entire year) and T = 6 months (since P and Q left the business after 6 months).

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

Therefore, the correct answer is 6 months.

This problem has been solved

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