In a class of 40 students , each one plays either Tennis or Badminton or both. If 28 plays Tennis and 26 play Badminton ,find
How many play Badminton only.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
We know that there are 40 students in total, and each student plays either Tennis, Badminton, or both.

### Step 2: Define variables
Let:
- \( x \) = the number of students who play both Tennis and Badminton.

### Step 3: Write down the total number of students
The total number of students is given as 40.

### Step 4: Write the equation based on the information provided
We know:
- 28 students play Tennis.
- 26 students play Badminton.

The equation can be set up as:
\[ \text{Total students} = (\text{Only Tennis}) + (\text{Only Badminton}) + (\text{Both}) \]
This can be expressed as:
\[ 40 = (28 - x) + (26 - x) + x \]

### Step 5: Simplify the equation
Now, simplify the equation:
\[ 40 = 28 + 26 - x \]
\[ 40 = 54 - x \]

### Step 6: Solve for \( x \)
Rearranging the equation gives:
\[ x = 54 - 40 \]
\[ x = 14 \]
So, 14 students play both Tennis and Badminton.

### Step 7: Find the number of students who play only Badminton
To find the number of students who play only Badminton, we can use the total number of Badminton players:
\[ \text{Only Badminton} = \text{Total Badminton players} - \text{Both} \]
\[ \text{Only Badminton} = 26 - 14 \]
\[ \text{Only Badminton} = 12 \]

### Final Answer
Thus, the number of students who play only Badminton is **12**.

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