Question : 15 men take 20 days to complete a job, working 8 hours a day. The number of hours a day that 20 men should take to complete the job in 12 days.
Option 1: 5 hours
Option 2: 10 hours
Option 3: 15 hours
Option 4: 18 hours
Correct Answer: 10 hours
Solution :
Given that 15 men can complete a job in 20 days, working 8 hours a day.
$⇒15 \times 20 \times 8 \times r = 1$
Where $r$ is the rate of work.
The number of hours a day that 20 men should take to complete the job in 12 days. Let's assume that each man works $h$ hours per day.
$⇒20 \times 12 \times h \times r = 1$
Equating the two expressions for $r$,
$⇒15 \times 20 \times 8 \times r = 20 \times 12 \times h \times r$
$⇒h = \frac{15 \times 20 \times 8}{20 \times 12}=10$
Therefore, each man needs to work $10$ hours per day.
Hence, the correct answer is 10 hours.
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