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    How many times starting at 1:00 pm would the minute and hour hands of a clock make an angle of 40° with each other in the next 6 hours?
    Question

    How many times starting at 1:00 pm would the minute and hour hands of a clock make an angle of 40° with each other in the next 6 hours?

    A.

    6

    B.

    7

    C.

    11

    D.

    12

    Correct option is C

    Problem Overview:

    We are asked to find how many times the angle between the hour and minute hands of a clock is exactly 40°between 1:00 pm and 7:00 pm — that is, in the next 6 hours.

    Concept Used:

    • In 12 hours, the hour and minute hands form any given angle (except 0° and 180°) 22 times.
    • So, in 6 hours, they form that angle 11 times.

    This rule holds true for any specific acute angle, like 40°.

    Final Answer: (C) 11

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