All the people in a locality read the daily newspaper Indian Express or Hindustan Times or both. If 120 read Indian Express and 150 read Hindustan Times and 36 read both, find :

(i) how many people are there in the locality;

(ii) how many people read only Indian Express.

Given:

People who read Indian Express: n(I) = 120

People who read Hindustan Times: n(H) = 150

People who read both: n(I ∩ H) = 36

(i) how many people are there in the locality

Since every person in the locality reads at least one of the two papers, the total population is equal to the union of the two sets, n(I ∪ H).

n(I ∪ H) = n(I) + n(H) − n(I ∩ H)

Substituting the values in above, we get:

n(I ∪ H) = 120 + 150 - 36

n(I ∪ H) = 270 - 36

n(I ∪ H) = 234

∴ Total people in the locality = 234.

(ii) how many people read only Indian Express

This represents the set I - H, consisting of people who read Indian Express but do not read Hindustan Times.

n(I - H) = n(I) - n(I ∩ H)

Substituting the values in above, we get:

n(I - H) = 120 - 36

n(I - H) = 84

∴ People who read only Indian Express = 84.

The Venn diagram is shown below: