According to a survey conducted in a neighbourhood, at least 70% of the people read the Hindu, at least 75% of the people read the Times of India and at least 80% of the people read the Deccan Chronicle. What is the minimum percentage of people in the neighbourhood, who read all three newspapers?

Let the number of people who read exactly one newspaper be ‘a’, the number of people who read exactly two newspapers be ‘b’ and the number of people who read exactly three newspapers be ‘c’.
So, a + b + c = 100%
a + 2b + 3c >= 70% + 75% + 80% = 225%
=> b + 2c >= 125
To find the minimum percentage of people who read all three newspapers, we have to minimize ‘c’. So, we have to maximize ‘b’.

Let a = 0 => b+c = 100 and b+2c >= 125
=> c >= 25
So, the minimum value of ‘c’ is 25. In this case, b = 75 and a = 0
So, at least 25% of the people in the neighbourhood read all the three newspapers.