The following questions are based on the information given below :
An advertising agency finds that of its 170 clients, 115 read Indian Express, 110 read The Hindu and 130 read Times of India. Also 85 read Indian Express and Times of India, 75 read Indian Express and The Hindu, 95 read The Hindu and Times of India and 70 read all the three
How many read only Indian Express ?
A. 15
B. 25
C. 5
D. 10

Options

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

Answer

To solve the problem of how many clients read only the Indian Express, we can use the principle of inclusion-exclusion and organize the information given into a Venn diagram.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Let \( A \) be the set of clients reading Indian Express (IE).
- Let \( B \) be the set of clients reading The Hindu (H).
- Let \( C \) be the set of clients reading Times of India (TOI).

From the problem, we have:
- \( |A| = 115 \) (clients reading Indian Express)
- \( |B| = 110 \) (clients reading The Hindu)
- \( |C| = 130 \) (clients reading Times of India)
- \( |A \cap B| = 75 \) (clients reading both IE and H)
- \( |A \cap C| = 85 \) (clients reading both IE and TOI)
- \( |B \cap C| = 95 \) (clients reading both H and TOI)
- \( |A \cap B \cap C| = 70 \) (clients reading all three newspapers)

2. **Calculate the Number of Clients Reading Only Indian Express:**
- To find the number of clients who read only Indian Express, we need to subtract those who read Indian Express in combination with other newspapers.
- The formula for clients reading only Indian Express is:
\[ |A \text{ only}| = |A| - (|A \cap B| + |A \cap C| - |A \cap B \cap C|) \]
- Plugging in the values:
\[ |A \text{ only}| = 115 - (75 + 85 - 70) \]
- Simplifying the equation:
\[ |A \text{ only}| = 115 - (75 + 85 - 70) = 115 - 90 = 25 \]

3. **Conclusion:**
- The number of clients who read only the Indian Express is \( 25 \).

### Final Answer:
The answer is **B. 25**.