A, 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?
Question
A, 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?
Solution
To solve this problem, we need to understand that the profit in a business is divided according to the capital and the time for which it is invested.
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Let's assume the initial capitals of A, B and C as 4x, 2x and 9x respectively.
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Since A halves his capital every quarter, his capital for the year would be: 4x (for the first quarter) + 2x (for the second quarter, as he halves his capital) + x (for the third quarter) + 0.5x (for the fourth quarter) = 7.5x
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B doubles his capital every quarter, so his capital for the year would be: 2x (for the first quarter) + 4x (for the second quarter) + 8x (for the third quarter) + 16x (for the fourth quarter) = 30x
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C does not change his capital, so his capital for the year would be: 9x (for each quarter) * 4 (for four quarters) = 36x
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The total capital invested for the year would be: 7.5x (A's capital) + 30x (B's capital) + 36x (C's capital) = 73.5x
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Now, we know that A's profit is Rs. 24000. Since profit is directly proportional to the capital invested, we can set up the following equation: 24000 / 7.5x = Total Profit / 73.5x
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Solving this equation for Total Profit, we get: Total Profit = 24000 * 73.5x / 7.5x
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Simplifying this, we get: Total Profit = Rs. 24000 * 73.5 / 7.5 = Rs. 235200
So, the total profit at the end of the year would be Rs. 235200.
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