In an examination, 80% of the students passed in English, 85% in Mathematics and 75% in both English and Mathematics. If 40 students failed in both the subjects, find the total number of students.

(a) 350

(b) 400

(c) 450

(d) 500

Solution:

Let x be the total number of students.

Let n(A) denotes the number of students passed in English and n(B) denotes the number of students passed in Maths.

n(A) = (80/100)x

n(B) = (85/100)x

n(A⋂B) = (75/100)x

Total number of students passed = n(A⋃B) = n(A) + n(B) – n(A⋂B)

= (80/100)x + (85/100)x – (75/100)x

= (90/100)x

= 9x/10

Number of students failed = x – (9x/10)

= x/10

Given 40 students failed in both the subjects.

So x/10 = 40

=> x = 400

Hence option b is the answer.

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