In an examination 34% failed in Mathematics and 42% falled in English. If 20% failed in both the subjects, the percentage of students who passed in both subjects was

Options

A. 0.54
B. 0.5
C. 0.44
D. 0.56

Answer

To solve the problem step by step, we can use the principle of inclusion-exclusion. Let's denote:

- \( A \): the set of students who failed in Mathematics
- \( B \): the set of students who failed in English

From the problem, we have the following information:

- \( P(A) = 34\% \) (percentage of students who failed in Mathematics)
- \( P(B) = 42\% \) (percentage of students who failed in English)
- \( P(A \cap B) = 20\% \) (percentage of students who failed in both subjects)

We want to find the percentage of students who passed in both subjects.

### Step 1: Calculate the percentage of students who failed in at least one subject
Using the inclusion-exclusion principle, we can find the percentage of students who failed in at least one subject:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Substituting the values we have:

\[ P(A \cup B) = 34\% + 42\% - 20\% \]

### Step 2: Perform the calculation
Now, we perform the calculation:

\[ P(A \cup B) = 34 + 42 - 20 = 56\% \]

This means that 56% of students failed in at least one subject.

### Step 3: Calculate the percentage of students who passed in both subjects
To find the percentage of students who passed in both subjects, we subtract the percentage of students who failed in at least one subject from 100%:

\[ \text{Percentage of students who passed in both subjects} = 100\% - P(A \cup B) \]

Substituting the value we calculated:

\[ \text{Percentage of students who passed in both subjects} = 100\% - 56\% = 44\% \]

### Final Answer
The percentage of students who passed in both subjects is **44%**.

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