Comprehension:
The following questions are based on the information given below:
In a school of 4000 students 3000 know English, 2000 know French and 500 know Hindi, 1500 know French and English, 300 know French and Hindi, 200 know English and Hindi and 50 know all the three languages.
How many know only two languages?

Options

A. 450
B. 500
C. 1850
D. 1580

Answer

To solve the problem, we will use the principle of inclusion-exclusion and a Venn diagram to organize the information about the students who know different languages.

### Step-by-Step Solution:

1. **Identify the given data:**
- Total students (U) = 4000
- Students who know English (E) = 3000
- Students who know French (F) = 2000
- Students who know Hindi (H) = 500
- Students who know both French and English (F ∩ E) = 1500
- Students who know both French and Hindi (F ∩ H) = 300
- Students who know both English and Hindi (E ∩ H) = 200
- Students who know all three languages (E ∩ F ∩ H) = 50

2. **Calculate the number of students who know only two languages:**
- **Only French and English (F ∩ E):**
\[ \text{Only French and English} = (F ∩ E) - (E ∩ F ∩ H) = 1500 - 50 = 1450 \]

- **Only French and Hindi (F ∩ H):**
\[ \text{Only French and Hindi} = (F ∩ H) - (E ∩ F ∩ H) = 300 - 50 = 250 \]

- **Only English and Hindi (E ∩ H):**
\[ \text{Only English and Hindi} = (E ∩ H) - (E ∩ F ∩ H) = 200 - 50 = 150 \]

3. **Add the numbers of students who know only two languages:**
\[ \text{Total students who know only two languages} = 1450 + 250 + 150 = 1850 \]

4. **Final answer:**
The number of students who know only two languages is **1850**.