In a circket charmpionship there are 36 matches. The number of teams if each plays one match with other, is

Options

A. 8
B. 9
C. 10
D. none of these

Answer

To solve the problem of finding the number of teams in a cricket championship where there are 36 matches, we can use the concept of combinations.

### Step-by-step Solution:

1. **Understanding the Problem**:
In a round-robin tournament, each team plays one match against every other team. If there are \( N \) teams, the number of matches played can be represented as the combination of \( N \) teams taken 2 at a time, which is denoted as \( \binom{N}{2} \).

2. **Setting Up the Equation**:
The formula for combinations is given by:
\[ \binom{N}{2} = \frac{N(N-1)}{2} \]
According to the problem, the total number of matches is 36. Therefore, we can set up the equation:
\[ \frac{N(N-1)}{2} = 36 \]

3. **Eliminating the Fraction**:
To eliminate the fraction, we multiply both sides of the equation by 2:
\[ N(N-1) = 72 \]

4. **Rearranging the Equation**:
We can rearrange this equation to form a standard quadratic equation:
\[ N^2 - N - 72 = 0 \]

5. **Factoring the Quadratic Equation**:
Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to -72 and add up to -1. The numbers are 8 and -9. Thus, we can factor the equation as:
\[ (N - 9)(N + 8) = 0 \]

6. **Finding the Roots**:
Setting each factor equal to zero gives us:
\[ N - 9 = 0 \quad \text{or} \quad N + 8 = 0 \]
Solving these, we find:
\[ N = 9 \quad \text{or} \quad N = -8 \]
Since the number of teams cannot be negative, we discard \( N = -8 \).

7. **Conclusion**:
Therefore, the number of teams \( N \) is:
\[ N = 9 \]

### Final Answer:
The number of teams is **9**.

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