In a town of 840 persons , 450 persons read Hindi, 300 read English and 200 read both. Then, the number of persons who read neither, is

Options

A. 210
B. 290
C. 180
D. 260

Explanation

To solve the problem step by step, we will use the principle of set theory. Let's denote:

- \( H \): the set of persons who read Hindi
- \( E \): the set of persons who read English
- \( |H| \): the number of persons who read Hindi = 450
- \( |E| \): the number of persons who read English = 300
- \( |H \cap E| \): the number of persons who read both Hindi and English = 200
- \( |H \cup E| \): the number of persons who read either Hindi or English or both
- \( N \): the total number of persons in the town = 840

### Step 1: Calculate the number of persons who read either Hindi or English or both

Using the formula for the union of two sets:

\[ |H \cup E| = |H| + |E| - |H \cap E| \]

Substituting the values:

\[ |H \cup E| = 450 + 300 - 200 \]

### Step 2: Perform the calculation

\[ |H \cup E| = 450 + 300 - 200 = 550 \]

### Step 3: Calculate the number of persons who read neither Hindi nor English

To find the number of persons who read neither, we subtract the number of persons who read either Hindi or English from the total number of persons:

\[ \text{Number of persons who read neither} = N - |H \cup E| \]

Substituting the values:

\[ \text{Number of persons who read neither} = 840 - 550 \]

### Step 4: Perform the final calculation

\[ \text{Number of persons who read neither} = 840 - 550 = 290 \]

### Final Answer

The number of persons who read neither Hindi nor English is **290**.

---