sandy wrote:
In a factory, machine A operates on a cycle of 20 hours of work followed by 4 hours of rest,and machine B operates on a cycle of 40 hours of work followed by 8 hours of rest. Last week, the two machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. On which days during that time period was there a time when both machines were at rest?
Indicate all such days.A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
F. Saturday
Practice Questions
Question: 19
Page: 207
For Machine A: For 20 hours of work, it takes 4 hours rest
=> In a span of 24 hours, the last 4 hours are for rest ... (i)
For Machine B: For 40 hours of work, it takes 8 hours rest
=> In a span of 48 hours, the last 8 hours are for rest ... (ii)
Thus, for the last 4 hours (out of the 8 hours) when Machine B is at rest, Machine A is also at rest.
This scenario occurs at the end of the 2nd day from when both A and B have started to work together
Thus, in every 2 days (48 hours), both machines are at rest in the last 4 hours
The machines start on Monday 12 noon
# First time both rest are the last 4 hrs of the 2nd day i.e. 8 am to 12 noon of
Wednesday(after this, both start working together from 12 noon of Wednesday)
# Thus, the second time both rest are the last 4 hrs of the 2nd day from Wednesday i.e. 8 am to 12 noon of
FridayThere would be no more opportunities of resting together since they work only till Saturday.
Answers: C and E
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