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    ​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 we
    Question

    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?

    A.

    275

    B.

    250

    C.

    175

    D.

    225

    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:

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

    Solution:

    A+OBoth=100+15075=175Neither=400175=225Final Answer: 225A + O - \text{Both} = 100 + 150 - 75 = 175 \\\text{Neither} = 400 - 175 = 225 \\\textbf{Final Answer:} \\\ \\\boxed{225}

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