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 ,
how many people are there in the locality.

Answer

To solve the problem, we will use the principle of inclusion-exclusion for sets. Here’s a step-by-step solution:

### Step 1: Define the Sets
Let:
- \( I \) = Set of people who read Indian Express
- \( H \) = Set of people who read Hindustan Times

### Step 2: Identify the Given Data
From the problem statement, we have:
- Number of people who read Indian Express, \( |I| = 120 \)
- Number of people who read Hindustan Times, \( |H| = 150 \)
- Number of people who read both newspapers, \( |I \cap H| = 36 \)

### Step 3: Use the Inclusion-Exclusion Principle
To find the total number of people who read at least one of the newspapers (i.e., the union of the two sets), we use the formula:
\[ |I \cup H| = |I| + |H| - |I \cap H| \]

### Step 4: Substitute the Values
Now, substitute the values we have into the formula:
\[ |I \cup H| = 120 + 150 - 36 \]

### Step 5: Perform the Calculation
Calculate the right-hand side:
\[ |I \cup H| = 270 - 36 = 234 \]

### Conclusion
Thus, the total number of people in the locality is \( \boxed{234} \).

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