In a group of 100 children, 62 like pizza, 47 like burger and 36 like both. Find the number of students who like pizza but not burger.

Options

A. 26
B. 15
C. 36
D. 30

Answer

To solve the problem, we can use the principle of inclusion-exclusion. Let's denote:

- \( P \) = number of children who like pizza = 62
- \( B \) = number of children who like burgers = 47
- \( P \cap B \) = number of children who like both pizza and burgers = 36

We need to find the number of students who like pizza but not burgers, which can be represented as \( P - (P \cap B) \).

### Step-by-Step Solution:

1. **Identify the total number of children who like pizza**:
\[ P = 62 \]

2. **Identify the number of children who like both pizza and burgers**:
\[ P \cap B = 36 \]

3. **Calculate the number of children who like pizza but not burgers**:
\[ \text{Number of children who like pizza but not burgers} = P - (P \cap B) \]
Substituting the values:
\[ = 62 - 36 \]
\[ = 26 \]

Thus, the number of students who like pizza but not burgers is **26**.