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Select the correct answerA, B and C started a business with their capitals in the ratio 4 : 2 : 9. at the end of every quarter, A halves his capital, whereas B doubles his capital and C leaves his capital unchanged. If at the end of a year, A’s profit was Rs.24000 , then what is the total profit?Options230,400235,200216,000225,600

Question

Select the correct answerA, B and C started a business with their capitals in the ratio 4 : 2 : 9. at the end of every quarter, A halves his capital, whereas B doubles his capital and C leaves his capital unchanged. If at the end of a year, A’s profit was Rs.24000 , then what is the total profit?Options230,400235,200216,000225,600

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Solution

The problem involves understanding the distribution of profits in a business based on the capital invested and the changes in the capital over time.

Step 1: Understand the initial capital ratio The initial capitals of A, B and C are in the ratio 4:2:9.

Step 2: Understand the changes in capital Every quarter (i.e., every 3 months), A halves his capital, B doubles his capital, and C leaves his capital unchanged. This happens 4 times in a year.

Step 3: Calculate the effective capital ratio We need to calculate the effective capital contributed by A, B, and C over the year.

For A, the capital halves every quarter. So, the effective capital of A over the year is 4 + 4/2 + 4/4 + 4/8 = 4 + 2 + 1 + 0.5 = 7.5.

For B, the capital doubles every quarter. So, the effective capital of B over the year is 2 + 22 + 24 + 2*8 = 2 + 4 + 8 + 16 = 30.

For C, the capital remains the same every quarter. So, the effective capital of C over the year is 9 + 9 + 9 + 9 = 36.

So, the effective capital ratio of A, B, and C over the year is 7.5:30:36.

Step 4: Calculate the total profit We know that A's profit is Rs. 24000. The profit is distributed in the ratio of the effective capital. So, the total profit is (24000 / 7.5) * (7.5 + 30 + 36) = Rs. 230400.

So, the correct answer is Rs. 230400.

This problem has been solved

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