Competitive Exam Analysis: Section Pass Rates

Key information provided:

• Passed Section A: 80%
• Passed Section B: 77%
• Failed Both Sections: 18%
• Passed Both Sections (Count): 1425

Calculating Percentage Passed in Both Sections

Candidates passing at least one section are those not failing both.

Percentage Passed (At Least One) = 100% - Percentage Failed Both

Percentage Passed (At Least One) = 100% - 18% = 82%

Let $P(A)$ denote the percentage passed in Section A, $P(B)$ the percentage passed in Section B, and $P(A \cap B)$ the percentage passed in both. The percentage passed in at least one section is $P(A \cup B)$.

Using the inclusion-exclusion principle:

Substitute known values:

$82\% = 80\% + 77\% - P(A \cap B)$

$82\% = 157\% - P(A \cap B)$

Solve for the percentage passed in both sections:

$P(A \cap B) = 157\% - 82\% = 75\%$

Finding Total Candidates

We established that 75% of total candidates passed both sections. This corresponds to 1425 students.

Let $T$ represent the total number of candidates.

$75\% \times T = 1425$

Convert percentage to decimal for calculation:

$0.75 \times T = 1425$

Solve for $T$:

$T = \frac{1425}{0.75}$

$T = \frac{1425}{3/4}$

$T = 1425 \times \frac{4}{3}$

$T = 475 \times 4$

$T = 1900$

Thus, 1900 candidates appeared for the examination.