Question : A, B, and C started a business with their investments in the ratio 1 : 2 : 4. After 6 months A increased his capital by 50% and B invested twice the amount as before, while C withdrew $\frac{1}{4}$th of his investment. The ratio of their profits at the end of the year was:
Option 1: 10 : 5 : 9
Option 2: 5 : 12 : 14
Option 3: 6 : 9 : 17
Option 4: 5 : 14 : 16
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Correct Answer: 5 : 12 : 14
Solution : The ratio of investments of A, B, and C = 1 : 2 : 4 Let the investments of A, B, and C be k, 2k, and 4k. Ratio of profit = Ratio of investment × Ratio of time The ratio of equivalent capitals of A, B, and C for 1 year = (k × 6 + $\frac{3}{2}$k × 6) : ( 2k × 6 + 4k × 6 ) : ( 4k × 6 + 3k × 6 ) The ratio of profits of A, B, and C for 1 year = 15k : 36k : 42k The ratio of profits of A, B, and C for 1 year = 5 : 12 : 14 Hence, the correct answer is 5 : 12 : 14.
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Question : A, B, and C entered into a business and their investment ratio was 5 : 4 : 3. After 4 months B invested Rs. 1,000 more and after 8 months C invested Rs. 2,000 more. At the end of one year, the profit ratio was 15 : 14 : 11, then the investment of C at the beginning was:
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