Question : Three boxes of capacities 24 kg, 36 kg, and 84 kg are filled with three varieties of wheat A, B, and C respectively. All three boxes were emptied, the three types of wheat were thoroughly mixed, and the mixture was put back in the three boxes. How many kilograms of type A wheat would be in the third box (in kg)?
Option 1: 10 kg
Option 2: 12 kg
Option 3: 14 kg
Option 4: 16 kg
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Correct Answer: 14 kg
Solution :
The mixture of A, B and C, according to the capacities of the boxes they were in, is in a ratio of $24 : 36 : 84 = 2 : 3 : 7$
Part of A in the mixture $=\frac{2}{2 + 3 + 7}= \frac{2}{12}$
According to the capacity of the third box, the amount of type A wheat in the third box
$=\frac{2}{12} × 84 = 14$ kg
Hence, the correct answer is 14 kg.
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