In an examination 70% of the candidates passed in English. 80% passed in Mathematics. 10% failed in both the subjects. If 144 candidates pased in both, the total number of candidates was :

Options

A. 125
B. 200
C. 240
D. 375

Answer

To solve the problem step by step, we can use the information provided in the question:

1. **Understanding the percentages**:
- Let the total number of candidates be \( x \).
- 70% of candidates passed in English: \( 0.7x \)
- 80% of candidates passed in Mathematics: \( 0.8x \)
- 10% of candidates failed in both subjects: \( 0.1x \)

2. **Finding the candidates who passed at least one subject**:
- Since 10% failed in both subjects, the percentage of candidates who passed at least one subject is:
\[ 100\% - 10\% = 90\% \]
- Therefore, the number of candidates who passed at least one subject is:
\[ 0.9x \]

3. **Using the principle of inclusion-exclusion**:
- According to the principle of inclusion-exclusion for two sets (those who passed English and those who passed Mathematics):
\[ \text{Number of candidates who passed in English} + \text{Number of candidates who passed in Mathematics} - \text{Number of candidates who passed in both} = \text{Number of candidates who passed at least one subject} \]
- Substituting the known values:
\[ 0.7x + 0.8x - \text{Number of candidates who passed in both} = 0.9x \]

4. **Letting \( y \) be the number of candidates who passed in both subjects**:
- We know from the problem that \( y = 144 \).
- Therefore, we can rewrite the equation:
\[ 0.7x + 0.8x - 144 = 0.9x \]

5. **Simplifying the equation**:
- Combine like terms:
\[ 1.5x - 144 = 0.9x \]
- Rearranging gives:
\[ 1.5x - 0.9x = 144 \]
\[ 0.6x = 144 \]

6. **Solving for \( x \)**:
- Divide both sides by 0.6:
\[ x = \frac{144}{0.6} = 240 \]

Thus, the total number of candidates is \( \boxed{240} \).