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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