The difference between two positive integers is 63, and they are in the ratio 2:5. The smaller integer is:

Let the two integers be 2k and 5k (some positive k). Their difference is 5k − 2k = 3k = 63, so k = 21. The smaller is 2k = 42 and the larger is 5k = 105 (check: 105 − 42 = 63 ✓, ratio 42:105 = 2:5 ✓).