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
Approach Solution - 1
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 = \( \frac{16}{100} \times 100 = 16 \).
Approach Solution -2
Step 1: Given Information
We are given the following percentages:
- 62% of the candidates failed in English.
- 42% of the candidates failed in Mathematics.
- 20% of the candidates failed in both English and Mathematics.
We need to find the number of candidates who passed in both subjects.
Step 2: Total Percentage of Candidates
Let the total number of candidates be \( 100 \) (as percentages are given). Therefore, we can represent the following:
- 62% failed in English, so 38% passed in English.
- 42% failed in Mathematics, so 58% passed in Mathematics.
- 20% failed in both subjects, meaning those candidates are included in both the English and Mathematics failure percentages.
Now, let's use the principle of inclusion-exclusion to calculate the percentage of candidates who passed in both subjects.
Step 3: Calculate Candidates Passing in Both Subjects
Let:
- \( A \) be the set of candidates who failed in English.
- \( B \) be the set of candidates who failed in Mathematics.
We are given:
- \( |A| = 62\% \),
- \( |B| = 42\% \),
- \( |A \cap B| = 20\% \) (candidates who failed in both subjects).
The percentage of candidates who failed in at least one subject is:
\[
|A \cup B| = |A| + |B| - |A \cap B| = 62\% + 42\% - 20\% = 84\%.
\]
Thus, 84% of candidates failed in at least one subject. Therefore, the percentage of candidates who passed in both subjects is:
\[
100\% - 84\% = 16\%.
\]
Step 4: Conclusion
The percentage of candidates who passed in both English and Mathematics is 16%.
The correct answer is: 16%
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