Answer: Option C
A sub-duplicate ratio is a type of ratio that is derived from the original ratio by dividing both the numerator and denominator by the same value. In other words, the sub-duplicate ratio is obtained by dividing the original ratio by the greatest common factor (GCF) of the numerator and denominator.
Let's consider the original ratio of 1:4. The GCF of 1 and 4 is 1, so dividing both the numerator and denominator by 1, we get 1/1 : 4/1 = 1 : 4.
However, the sub-duplicate ratio can also be obtained by dividing both the numerator and denominator by their mean. The mean of the ratio 1:4 can be calculated as follows:
Mean = (1 + 4) / 2 = 2.5
Dividing both the numerator and denominator by the mean, we get 1/2.5 : 4/2.5 = 1 : 2.
Therefore, the sub-duplicate ratio of 1 : 4 is 1 : 2.
It's worth noting that the sub-duplicate ratio can also be obtained by dividing both the numerator and denominator by their geometric mean. The geometric mean of the ratio 1:4 can be calculated as follows:
Geometric Mean = √(1 * 4) = 2
Dividing both the numerator and denominator by the geometric mean, we get 1/2 : 4/2 = 1 : 2.
In conclusion, the sub-duplicate ratio of 1 : 4 is 1 : 2, as shown by both the GCF method and the mean and geometric mean methods.