In a class of 43 students at least every one of them offers physics or geography. If 27 of them offers physics and 31 offers geography, how many of them offer both physics and geography

Answer 1

Offer? I think you mean "... 43 students ... takes physics or geography ... "
The school offers the courses. The students take the courses.

Answer 2

27+31-x = 43
Time to review set unions and intersections and Venn diagrams...