A group of 30 men participate in a sruvey on language skills. The number of men whoe know both English and Hindi was equal to the number of men who know neither of these language . The number of men who know English is 4 more than those who know Hindi. How many know Hindi?

Options

A. 11
B. 12
C. 13
D. 14

Explanation

To solve the problem step by step, we will define variables and use the information provided in the question.

### Step 1: Define Variables
Let:
- \( x \) = number of men who know Hindi
- \( x + 4 \) = number of men who know English (since the number of men who know English is 4 more than those who know Hindi)

### Step 2: Set Up the Equation
According to the problem, the number of men who know both English and Hindi is equal to the number of men who know neither language. Let’s denote:
- \( n(E \cap H) \) = number of men who know both English and Hindi
- \( n(N) \) = number of men who know neither language

From the problem, we know:
- \( n(E \cap H) = n(N) \)

### Step 3: Total Number of Men
The total number of men surveyed is 30. We can express this as:
\[ n(E) + n(H) - n(E \cap H) + n(N) = 30 \]
Substituting the known values:
\[ (x + 4) + x - n(E \cap H) + n(E \cap H) = 30 \]
This simplifies to:
\[ 2x + 4 = 30 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):
\[ 2x + 4 = 30 \]
Subtract 4 from both sides:
\[ 2x = 26 \]
Now, divide by 2:
\[ x = 13 \]

### Step 5: Conclusion
The number of men who know Hindi is \( x = 13 \).

### Final Answer
Thus, the number of men who know Hindi is **13**.

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