. A clock loses 5 min every hour and was set right at 10:00am on a Sunday. When will it
show the correct time again?
Answers
Answer:
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Answer:
A watch loses 5 min every hour. Which means if a watch is 5 min late in first one hour then it will be late by 10 min in second hour and by 15 min in the third hour. It will show the correct time only when it is late by 24 hours because then it will show a repeated time though a day late. Hence we need to find the no. Of hours corresponding to which the watch becomes 24 hours late. Since it says that 5 min is lost each hours . Let the no. Of hours be n after which the watch loses 1400 min since span of 24 hours has 1440 mins in it. The series is as follows :
5, 10, 15, 20,...,1440 which represent 5 min late in first hour, 10 min late in second hour and so on.. We find that the series is in A.P (arithithmatic progression) with the first term as 5 and last term as 1440. ( when the watch is late by 1440 min , it shows the correct time , though its a day late) and a common difference of 5.
In AP last term L = a +nd-d
Where a is the first term
n is the no. Of terms
d is the common difference
Putting
a = 5
d = 5 and
L = 1440
We get n= 288
It means that after a period of 288 hrs the watch becomes late by 24 hrs.
Hence after 288 hrs or after 12 days the watch shows the right time.
Hope it helps!!
Have a nice day :)