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:
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:
Show Hint
- 11
- 16
- 18
- None of these
The Correct Option is B
Solution and Explanation
Step 1: Calculate the percentage of candidates who failed in either English or Mathematics or both
Percentage failed in English or Mathematics or both = Percentage failed in English + Percentage failed in Mathematics - Percentage failed in both = 62% + 42% - 20% = 84%
Step 2: Calculate the percentage of candidates who passed in both subjects
Percentage passed in both subjects = 100% - Percentage failed in English or Mathematics or both = 100% - 84% = 16%
Step 3: Assume the total number of candidates
Let the total number of candidates be \( x \).
Step 4: Calculate the number of candidates who passed in both subjects
Number of candidates who passed in both subjects = 16% of \( x \) = \( \frac{16}{100} \times x \)
Step 5: Relate the number to the options
Since the options are whole numbers, we can assume \( x = 100 \) for simplicity. Then, the number of candidates who passed in both subjects = \( \frac{16}{100} \times 100 = 16 \).
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