Problem: According to Exodus 40:2, Moses took the census of the people of Israel the “first day of the first month.” But in Numbers, the same census, yielding the same number of 603,550, was taken on “the first day of the second month” (Num. 1:1).
Solution: These are apparently two different censuses for two different purposes. The first one (Ex. 38) was for religious purposes and the second for military purposes. The first one was connected with the “inventory of the tabernacle” (Ex. 38:21), that is, a collection of the offering used for the tabernacle. The later one had to do with how many men were “able to go to war in Israel” (Num. 1:3). Both yield the same result since they were taken so close together.