200 students appeared in a specific examination. There were 80 students who failed in Mathematics. 160 students passed in Physics. 30 students failed in Chemistry. 30 students failed in Mathematics and Physics. 15 students failed in Mathematics and Chemistry. 10 students failed in Physics and Chemistry. 100 students passed in all three subjects. How many students failed in only one subject?

Option 2 : 55

Concept used:

The Venn diagram is constructed based on the number of students who failed the exam.

[ alt="venn dia" src="//storage.googleapis.com/tb-img/production/21/02/venn%20dia.PNG" style="width: 380px; height: 285px;">

Calculation:

From the given information we get,

C + D + G + F = 30

G + E = 30

G + F = 15

D + G = 10

B + E + G + F = 80

From the data we can deduce the following:

A + E + G + D = 200 - 160 = 40

C + A + D = 20

A + E + B = 70

B + F + C = 60

Substituting and solving we get,

A = 5, B = 40,  E = 25, G = 5, F = 10, C = 10, D = 5

Number of people who failed in only one subject = A + B + C = 5 + 40 + 10 = 55