Question

In an examination, it was found that every student has failed in at least one subject out of the three subjects: English, Maths and Science. 28 students failed in English, 30 students failed in Maths and 32 students failed in Science. 6 students failed in English and Maths, 8 students failed in Maths and Science and 10 students failed in English and Science. The number of students who failed in only one subject is 54. Also, 20 students failed only in Maths.

Determine the number of students who appeared in the examination.

• A. 20
• B. 40
• C. 30
• D. 70

Answer 1

The correct option is D 70

No. of students who failed only in Maths= 20 (Given)

According to condition given,

Students who failed in Maths and English only + Students who failed in Science and Maths only + Students who failed in all three papers= 30-20= 10.

Therefore, 6+8-x=10 (x being the number of students who failed in all three subjects)

Solving the above equation gives x=4

Student who failed in:-

All three subjects=4

Maths and English only=2

Maths and Science only=4

Science and English only=6

English only=16

Science only=18

Therefore total no. of students= 16+18+20+2+4+6+4=70

Hence answer option d.