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 at least one language?
A. 3500
B. 3000
C. 1850
D. 3550

Options

A. A
B. B
C. C
D. D

Answer

To find out how many students know at least one language, we can use the principle of inclusion-exclusion. Let's break down the problem step by step.

### Step 1: Define the variables
Let:
- \( E \) = number of students who know English = 3000
- \( F \) = number of students who know French = 2000
- \( H \) = number of students who know Hindi = 500
- \( EF \) = number of students who know both English and French = 1500
- \( FH \) = number of students who know both French and Hindi = 300
- \( EH \) = number of students who know both English and Hindi = 200
- \( EFH \) = number of students who know all three languages = 50

### Step 2: Apply the inclusion-exclusion principle
The formula for the number of students who know at least one language is given by:

\[ |E \cup F \cup H| = |E| + |F| + |H| - |EF| - |FH| - |EH| + |EFH| \]

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ |E \cup F \cup H| = 3000 + 2000 + 500 - 1500 - 300 - 200 + 50 \]

### Step 4: Calculate the total
Now, let's perform the calculations step by step:

1. Add the number of students who know each language:
\[ 3000 + 2000 + 500 = 5500 \]

2. Subtract the students who know two languages:
\[ 5500 - 1500 - 300 - 200 = 4500 \]

3. Add back the students who know all three languages:
\[ 4500 + 50 = 4550 \]

### Step 5: Final calculation
The total number of students who know at least one language is:
\[ |E \cup F \cup H| = 4550 \]

### Conclusion
The number of students who know at least one language is **3550**. Therefore, the correct answer is **D. 3550**.