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    Six boys can complete a piece of work in 42 hours. In how many hours will 14 boys complete the same piece of work?
    Question

    Six boys can complete a piece of work in 42 hours. In how many hours will 14 boys complete the same piece of work?

    A.

    18

    B.

    17

    C.

    16

    D.

    15

    Correct option is A

    Given:

    1. 6 boys can complete the work in 42 hours.

    2. We need to find how long it will take for 14 boys to complete the same work.

    Formula Used:

    Work done is inversely proportional to the number of workers when the total amount of work is constant:

    Work Hours1×Number of Workers1=Work Hours2×Number of Workers2\text{Work Hours}_1 \times \text{Number of Workers}_1 = \text{Work Hours}_2 \times \text{Number of Workers}_2

    1. Use the formula:

    6×42=14×Work Hours26 \times 42 = 14 \times \text{Work Hours}_2

    Work Hours2=6×4214\text{Work Hours}_2 = \frac{6 \times 42}{14}

    3. Simplify:

    Work Hours2=25214=18 hours\text{Work Hours}_2 = \frac{252}{14} = 18 \, \text{hours}

    Final Answer:

    14 boys will complete the same piece of work in 18 hours.

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