28 teachers of a school either teach mathematics or physics 20 of them mathematics white 4 teach both the subjects . The number of teachers teching physics only ,is

Options

A. `12`
B. `8`
C. `16`
D. none of these

Answer

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

- Total number of teachers = 28
- Number of teachers teaching Mathematics (M) = 20
- Number of teachers teaching both Mathematics and Physics (B) = 4

We need to find the number of teachers teaching Physics only (P).

### Step 1: Calculate the number of teachers teaching only Mathematics.

The number of teachers teaching only Mathematics can be calculated as follows:

\[ \text{Teachers teaching only Mathematics} = M - B \]

Substituting the values:

\[ \text{Teachers teaching only Mathematics} = 20 - 4 = 16 \]

### Step 2: Calculate the total number of teachers teaching Physics.

We know that the total number of teachers is the sum of those teaching only Mathematics, those teaching only Physics, and those teaching both subjects. Let \( P \) be the number of teachers teaching Physics (including those who teach both subjects).

Thus, we can write:

\[ \text{Total teachers} = \text{Teachers teaching only Mathematics} + \text{Teachers teaching only Physics} + \text{Teachers teaching both} \]

Substituting the known values:

\[ 28 = 16 + P + 4 \]

### Step 3: Simplify the equation to find \( P \).

Now we can simplify the equation:

\[ 28 = 20 + P \]

Subtracting 20 from both sides gives:

\[ P = 28 - 20 = 8 \]

### Step 4: Calculate the number of teachers teaching only Physics.

Now, we know that \( P \) includes both the teachers teaching only Physics and those teaching both subjects. Therefore, the number of teachers teaching only Physics can be calculated as follows:

\[ \text{Teachers teaching only Physics} = P - B \]

Substituting the values we have:

\[ \text{Teachers teaching only Physics} = 8 - 4 = 4 \]

### Final Answer:

The number of teachers teaching Physics only is **4**.

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