​In a school survey of 400 students 100 were taking apple juice, 150 orange juice and 75 were taking both apple and orange juice. How many students were taking neither apple nor orange juice?​

Correct option is D

Given:
Total students = 400
Students taking Apple juice (A) = 100
Students taking Orange juice (O) = 150
Students taking both Apple and Orange juice = 75
We are to find the number of students taking neither Apple nor Orange juice.

Formula:

$$\text{Only A or O or both} = A + O - \text{Both} \\\text{Neither} = \text{Total} - (A + O - \text{Both}) \\$$

Solution:

$$A + O - \text{Both} = 100 + 150 - 75 = 175 \\\text{Neither} = 400 - 175 = 225 \\\textbf{Final Answer:} \\\ \\\boxed{225}$$​