In a survey of 100 students, the number of students studying the various languages were found to be: English only 18, English but not Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, no language 24. Find:
How many students were studying English and Hindi?

Answer

To solve the problem step by step, we will first organize the given information and then use it to find the number of students studying both English and Hindi.

### Step 1: Organize the given data
We have the following information from the survey of 100 students:
- English only: 18
- English but not Hindi: 23
- English and Sanskrit: 8
- Total studying English: 26
- Total studying Sanskrit: 48
- Sanskrit and Hindi: 8
- No language: 24

### Step 2: Define the variables
Let:
- A = Students studying only English
- B = Students studying English and Hindi
- C = Students studying only Hindi
- D = Students studying English and Sanskrit
- E = Students studying only Sanskrit
- F = Students studying Sanskrit and Hindi
- G = Students studying only Hindi
- H = Students studying no language

### Step 3: Set up equations based on the information
From the information provided, we can set up the following equations:
1. A = 18 (English only)
2. A + D = 23 (English but not Hindi)
3. D + B = 8 (English and Sanskrit)
4. A + B + D = 26 (Total studying English)
5. E + F = 48 (Total studying Sanskrit)
6. H = 24 (No language)

### Step 4: Calculate the values
From equation 1, we know A = 18.

From equation 2:
- A + D = 23
- 18 + D = 23
- D = 23 - 18 = 5

From equation 4:
- A + B + D = 26
- 18 + B + 5 = 26
- B = 26 - 18 - 5 = 3

### Step 5: Conclusion
The number of students studying both English and Hindi (B) is 3.

### Final Answer
Thus, the number of students studying English and Hindi is **3**.