Question

In a class of 100 students, 40 like mathematics, 50 like physics, and 80 like English. The number of students who like only two subjects is 60. How many students like all the three subjects?

• A. 5
• B. 12
• C. 10
• D. 8

Answer 1

The correct option is A 5

Let's represent the situation as a Venn diagram and divide the sections with letters.

The number of students who like all the three subjects = x

40 students like mathematics:
a + b + q + x = 40

50 students like physics:
a + c + p + x = 50

80 students like English:
b + c + r + x = 80

Let's add all the three equations.
2(a + b + c) + p + q + r + 3x = 170

$\text{Number of students who like two subjects = 60}$
a + b + c = 60

Let's substitute the value of a + b + c in the above equation.
2(60) + p + q + r + 3x = 170
120 + p + q + r + 3x = 170
p + q + r + 3x = 170 – 120 = 50
p + q + r = 50 – 3x

$\text{Total number of students in the class = 100}$
p + q + r + a + b + c + x = 100
p + q + r + 60 + x = 100
50 – 3x + 60 + x = 100
110 – 2x = 100
–2x = 100 – 110
–2x = –10
2x = 10
x = 5

5 students like all three subjects.