Question

In an examination, 82% of students passed in Mathematics, 70% passed in Science and 13% failed in both the subjects. If 299 students passed in both the subjects, then the total number of students who appeared in the examination is:

• A. 440
• B. 460
• C. 500
• D. 520

Hint:

In questions involving percentages, always use the principle of inclusion-exclusion to avoid double counting.

Answer 1

The Correct Option is C

Let the total number of students be \( N \). - 82% of \( N \) passed in Mathematics, so \( 0.82N \) passed in Mathematics. - 70% of \( N \) passed in Science, so \( 0.70N \) passed in Science. - 13% failed in both, so 87% passed at least one subject: \[ 0.87N \] Let \( x \) be the number of students who passed in both subjects. We are given that \( x = 299 \). Using the principle of inclusion-exclusion: \[ 0.82N + 0.70N - 299 = 0.87N \] Simplifying: \[ 1.52N - 299 = 0.87N \] \[ 1.52N - 0.87N = 299 \quad \Rightarrow \quad 0.65N = 299 \quad \Rightarrow \quad N = \frac{299}{0.65} = 460 \] Thus, the total number of students who appeared in the examination is \( 460 \).