Question:
Out of 205 students:
- 105 pass in English
- 70 pass in Mathematics
- 30 pass in both
How many students fail in both subjects?
Out of 205 students:
- 105 pass in English
- 70 pass in Mathematics
- 30 pass in both
How many students fail in both subjects?
- 105 pass in English
- 70 pass in Mathematics
- 30 pass in both
How many students fail in both subjects?
Show Hint
To find how many fail in both, subtract those who passed at least one subject from the total.
Updated On: May 20, 2025
- 60
- 145
- 175
- 30
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The Correct Option is A
Solution and Explanation
We use the principle of inclusion and exclusion.
Let:
- \( E \): Students passing English = 105
- \( M \): Students passing Mathematics = 70
- \( E \cap M \): Students passing both = 30
So, students who pass in at least one subject: \[ |E \cup M| = |E| + |M| - |E \cap M| = 105 + 70 - 30 = 145 \] Total students = 205 Hence, students who fail in both subjects: \[ 205 - 145 = \boxed{60} \]
- \( E \): Students passing English = 105
- \( M \): Students passing Mathematics = 70
- \( E \cap M \): Students passing both = 30
So, students who pass in at least one subject: \[ |E \cup M| = |E| + |M| - |E \cap M| = 105 + 70 - 30 = 145 \] Total students = 205 Hence, students who fail in both subjects: \[ 205 - 145 = \boxed{60} \]
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