Question

In an examinations 42% students failed in English and 52% failed in Mathematics. If 17% failed in both the subjects, the percentage of those who passed in both the subjects is

• A. 40%
• B. 27%
• C. 34%
• D. 23%

Hint:

Passed in both $= 100 - (\text{Fail}_1 + \text{Fail}_2 - \text{Fail}_{\text{both}}) = 100 - (42 + 52 - 17) = 23\%$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Using the Principle of Inclusion-Exclusion for two intersecting sets.

Step 2: Key Formula or Approach:
Let $E$ be the set of students failing English and $M$ be the set failing Mathematics:
\[P(E) = 42\%,\quad P(M) = 52\%,\quad P(E \cap M) = 17\%\] Total percentage of students who failed in at least one subject:
\[P(E \cup M) = P(E) + P(M) - P(E \cap M) = 42\% + 52\% - 17\% = 77\%\]

Step 3: Detailed Explanation:
The percentage of students who passed in both subjects:
\[\text{Passed in Both} = 100\% - P(E \cup M) = 100\% - 77\% = 23\%\]

Step 4: Final Answer:
Hence, the percentage of students who passed in both subjects is 23%.