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?
Solution: let the total number of students be x.
Number passed in one or both is given by : n( A U B) = n(A)+n(B) -n( A ^ B).
= 60% of x+65% of x-40% of x
= (60/100 * x + 65/100 * x - 40/100 * x)
= 85x/100 = 17x/20.
Failed in both = (x - 17x/20) = 3x/20.
.'. 3x/20 =90
x = 90*20/3 = 600.
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