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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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