JAMB Mathematics 2019 Paper

Concept:Set theory is used to find the number of students who took both subjects.Explanation:Let total students in the class be $n(P \cup B) = 50$.Let $n(P)=40$ be the number who offered Physics.Let $n(B)=30$ be the number who offered Biology.Let $x$ represent the number who offered both Physics and Biology, so $x = n(P \cap B)$.Students who offered Physics only $= 40 - x$.Students who offered Biology only $= 30 - x$.Since no student is left outside these two groups, the total is:$$(40 - x) + (30 - x) + x = 50$$Simplify:$$70 - x = 50$$Solve for $x$:$$x = 20$$Answer:B. 20