31 candidates appeared for an examination, 15 candidates passed in English, 15 candidates passed in Hindi, 20 candidates passed in Sanskrit. 3 candidates passed only in English. 4. candidates passed only in Hindi, 7 candidates passed only in Sanskrit. 2 candidates passed in all the three subiects How many candidates passed only in two subjects

Answer

To solve the problem, we will use the information given about the candidates who passed in different subjects and set up equations based on the data provided.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Let \( x \) be the number of candidates who passed only in English and Hindi.
- Let \( y \) be the number of candidates who passed only in English and Sanskrit.
- Let \( z \) be the number of candidates who passed only in Hindi and Sanskrit.

2. **Set Up the Known Values:**
- Candidates who passed only in English: 3
- Candidates who passed only in Hindi: 4
- Candidates who passed only in Sanskrit: 7
- Candidates who passed in all three subjects: 2

3. **Total Candidates Passing Each Subject:**
- Total passing in English: \( 3 + x + 2 + y = 15 \)
- Total passing in Hindi: \( 4 + x + 2 + z = 15 \)
- Total passing in Sanskrit: \( 7 + y + z + 2 = 20 \)

4. **Formulate the Equations:**
- From the English equation:
\[ 3 + x + 2 + y = 15 \implies x + y = 10 \quad \text{(Equation 1)} \]
- From the Hindi equation:
\[ 4 + x + 2 + z = 15 \implies x + z = 9 \quad \text{(Equation 2)} \]
- From the Sanskrit equation:
\[ 7 + y + z + 2 = 20 \implies y + z = 11 \quad \text{(Equation 3)} \]

5. **Solve the Equations:**
- We have three equations:
1. \( x + y = 10 \)
2. \( x + z = 9 \)
3. \( y + z = 11 \)

- From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 10 - x \]
- Substitute \( y \) into Equation 3:
\[ (10 - x) + z = 11 \implies z = 1 + x \quad \text{(Equation 4)} \]
- Substitute \( z \) from Equation 4 into Equation 2:
\[ x + (1 + x) = 9 \implies 2x + 1 = 9 \implies 2x = 8 \implies x = 4 \]
- Now substitute \( x = 4 \) back into Equations 1 and 4 to find \( y \) and \( z \):
\[ y = 10 - 4 = 6 \]
\[ z = 1 + 4 = 5 \]

6. **Calculate Candidates Passing Only in Two Subjects:**
- The total number of candidates who passed only in two subjects is:
\[ x + y + z = 4 + 6 + 5 = 15 \]

### Final Answer:
Therefore, the number of candidates who passed only in two subjects is **15**.