In a group of 15 people, 7 read Hindi, 8 read English and 3 read none of these language. How many people read Hindi and English both ?

Question

Accepted Answer

To determine how many people read both Hindi and English, we can use the principle of inclusion-exclusion. Let's break down the information given:

1. Total number of people in the group = 15
2. Number of people who read Hindi = 7
3. Number of people who read English = 8
4. Number of people who read neither Hindi nor English = 3

First, we calculate the number of people who read at least one of the two languages (Hindi or English):

Total people - People who read neither = 15 - 3 = 12

This means 12 people read at least one of the two languages. Now, using the principle of inclusion-exclusion:

Number of people who read at least one language = (Number of people who read Hindi) + (Number of people who read English) - (Number of people who read both Hindi and English)

Substituting the known values:

12 = 7 + 8 - (Number of people who read both Hindi and English)

12 = 15 - (Number of people who read both Hindi and English)

Number of people who read both Hindi and English = 15 - 12 = 3

Therefore, the correct answer is Option 2, which states that 3 people read both Hindi and English.

Explanation of why other options are incorrect:

1. Option 1 (0): This option suggests that no one reads both languages, which is incorrect because our calculation shows that 3 people do read both.

3. Option 3 (4): This option suggests that 4 people read both languages, which contradicts our calculation of 3 people.

4. Option 4 (5): This option suggests that 5 people read both languages, which is also incorrect based on our calculation.

Thus, the correct answer is Option 2, as it accurately reflects the number of people who read both Hindi and English.