In a survey conduced on 800 students of a school , 250 students were found to like tea and 300 like coffee , 150 like both tea and coffee .Find how many students like neither tea nor coffee ?

Explanation

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

**Step 1: Identify the given values.**
- Total number of students surveyed (N) = 800
- Number of students who like tea (T) = 250
- Number of students who like coffee (C) = 300
- Number of students who like both tea and coffee (B) = 150

**Step 2: Calculate the number of students who like either tea or coffee.**
To find the number of students who like either tea or coffee, we can use the principle of inclusion-exclusion:

\[ \text{Number of students who like tea or coffee} = T + C - B \]

Substituting the values we have:

\[ \text{Number of students who like tea or coffee} = 250 + 300 - 150 \]

Calculating this gives:

\[ = 400 \]

**Step 3: Calculate the number of students who like neither tea nor coffee.**
To find the number of students who like neither tea nor coffee, we subtract the number of students who like either tea or coffee from the total number of students surveyed:

\[ \text{Number of students who like neither tea nor coffee} = N - (\text{Number of students who like tea or coffee}) \]

Substituting the values we have:

\[ \text{Number of students who like neither tea nor coffee} = 800 - 400 \]

Calculating this gives:

\[ = 400 \]

**Final Answer:**
The number of students who like neither tea nor coffee is **400**.

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