In an examination, 25% candidates failed in English and 35 % students failed in Math. If 15 % candidates failed in both, what is the percentage of candidates who passed in both the subjects?

Options

A. 58 %
B. 55 %
C. 50 %
D. 45 %

Answer

To solve the problem, we will use the principle of inclusion-exclusion to find the percentage of candidates who passed in both subjects.

### Step-by-Step Solution:

1. **Define the Total Candidates**:
Assume the total number of candidates is 100.

2. **Identify Failures**:
- Candidates who failed in English = 25% of 100 = 25 candidates.
- Candidates who failed in Math = 35% of 100 = 35 candidates.
- Candidates who failed in both subjects = 15% of 100 = 15 candidates.

3. **Calculate Candidates Failing in Either Subject**:
Using the principle of inclusion-exclusion, we can find the total percentage of candidates who failed in at least one subject:
\[ \text{Failed in either subject} = (\text{Failed in English}) + (\text{Failed in Math}) - (\text{Failed in both}) \]
\[ = 25 + 35 - 15 = 45 \]
Therefore, 45 candidates failed in at least one subject.

4. **Calculate Candidates Passing in Both Subjects**:
To find the number of candidates who passed in both subjects, we subtract the number of candidates who failed in either subject from the total number of candidates:
\[ \text{Passed in both subjects} = \text{Total candidates} - \text{Failed in either subject} \]
\[ = 100 - 45 = 55 \]

5. **Calculate the Percentage of Candidates Passing in Both Subjects**:
The percentage of candidates who passed in both subjects is:
\[ \text{Percentage passed} = \left(\frac{\text{Passed in both subjects}}{\text{Total candidates}}\right) \times 100 \]
\[ = \left(\frac{55}{100}\right) \times 100 = 55\% \]

### Final Answer:
The percentage of candidates who passed in both subjects is **55%**.