If the standard deviation of Set B is 12.5, then what is the standard

If you add the same value to everything in a set, you don't change any of the distances within the set, so you don't change the standard deviation. So if 12.5 is the standard deviation of set B, then 12.5 is also the standard deviation of the set

2a/3, 2b/3, 2c/3, 2d/3, 2e/3

If you multiply every value in a set by a constant positive number, you correspondingly stretch out the distances in the set (or shrink them, if you multiply by something less than 1). So the standard deviation is also multiplied by that constant. So if we multiply every value in the set above by 3/2, to get set A, we'll be multiplying our standard deviation by 3/2, and the answer is (3/2)(12.5) = (3/2)(25/2) = 75/4 = 18.75.