Question

In an examination, 85% of the students passed in English, 80% passed in Mathematics and 75% passed in both English and Mathematics. If 50 students fail in both the subjects, then the total number of students who appear in the exam is:

• A. 500
• B. 400
• C. 600
• D. 300

Hint:

Use formula: $A + B - (A \cap B)$ for “at least one” type questions.

Answer 1

The Correct Option is A

Concept: Use inclusion-exclusion principle.
Step 1: Let total students = $x$.
Passed at least one subject: \[ 85% + 80% - 75% = 90% \]
Step 2: Students failing both.
\[ 100% - 90% = 10% \]
Step 3: Form equation.
\[ 10% { of } x = 50 \Rightarrow 0.1x = 50 \Rightarrow x = 500 \]
Hence, the total number of students is 500.