In an examination, 62% of the candidates failed in English, 42% in Mathematics and 20% in both. The number of those who passed in both the subjects is:
Step 1: Determine the proportion of candidates failing at least one subject (English, Mathematics, or both). This is computed as the sum of those failing English and those failing Mathematics, minus those failing both. Calculation: 62% + 42% - 20% = 84%.
Step 2: Calculate the proportion of candidates passing both subjects. This is the complement of failing at least one subject. Calculation: 100% - 84% = 16%.
Step 3: Establish a variable for the total candidate count. Let the total number of candidates be \( x \).
Step 4: Quantify the number of candidates passing both subjects. This is 16% of the total candidate count \( x \), represented as \( \frac{16}{100} \times x \).
Step 5: Align the result with available options. Given that the options are integers, setting \( x = 100 \) simplifies the calculation. Consequently, the number of candidates passing both subjects is \( \frac{16}{100} \times 100 = 16 \).