A clock is correct at midnight. From that moment it begins to lose one minute per hour. The clock stopped an
hour and a half ago showing 13.46. The clock runs for less than 24 hours. What is the correct time now?
Answers
The correct time now is 15:30
(the problem is solved by assuming that 13.46 implies 13 hours 46 minutes, if it means 13.46 as 13.46 hours, the same procedure can still be followed taking care of hours and minutes conversion)
-The clock stopped working one and half hour ago, hence 90 min correct time has passed since the clock stopped.
-Our aim is to find the correct time from given wrong time and add 90 min to get our current time
-Clock loses 1 min/hour.
Which implies it loses 1/60 minutes every minute.
Therefore we can say that it loses n/60 minutes every n minutes.
hence we can write, Tw = Tc - Tc/60
where, Tw = wrong time in minutes
Tc = correct time in minutes
( verify it and convince yourself the formula, by putting in values of correct time for example, if Tc = 60min i.e., 1 hour, then Tw = 59min )
-Now we have our wrong time as 13.46 which translates to 826 min, So we have Tw = 826min
-Use Tw in our equation to find Tc which turns out to be 840 min. This is exactly 14 hours.
-adding our 90 min or 1.5 hours, the correct time is 15.5 hours or 15:30 (15 hours 30 minutes)