The difference between two positive numbers is 50. The second number is 50 % smaller than the first one. What are the two numbers?

Let's call the numbers we are looking for a and b. From the question: a-b = 50 and b is 50% of a, which means that b = (50/100)a=0.5 a. Substituting this form of b in the first equation, we obtain: a-0.5a= 50 which is 0.5 a = 50. This leads to: a=50/0.5=50/(1/2)=50*2=100. Once a is known, b can be easily obtained from a-b=50 which becomes: b= a-50=100-50=50.Therefore the two numbers are: 100 and 50.