In a test, sixty percent students passed in Maths and 65% in History, 40% passed in both of these subjects. If 90 students failed in maths and history both, then what is the total number of students?

600

650

700

750

Explanation:

Let the total number of students be x.

Number passed in one or both is given by: n$\left(A\cup B\right)$ = n(A)+n(B) - n (A ^ B).

=> 60% of x + 65% of x - 40% of x.

=> (60/100 $\times$ x + 65/100 $\times$ x - 40/100 $\times$ x)

=> 85x/100 = 17x/20.

Failed in both = (x - 17x/20) = 3x/20.

=> 3x/20 = 90.

=> x = 90 $\times$ 20/3 = 600.