Clocks- Losing/Gaining of Time

In the previous article on clocks, we studied the two types of problems asked from this topic i.e. finding the time when the angle between the two hands is given and finding the angle between the 2 hands at a given time. In this article, we are going to discuss the third important concept of clocks i.e. losing and gaining of time.

Let us try understanding this concept with the help of an example.

If a watch indicates 9.20, when the correct time is 9.10, it is said to be 10 minutes too fast. And if it indicates 9.00, when the correct time is 9.10, it is said to be 10 minutes too slow.

Such kind of problems appear in exams very often, when a clock runs faster or slower than the expected pace.

Clock is running fast: It is also referred to as gaining time i.e. when a normal clock covers 60 minutes, a faster clock will cover more than 60 minutes.

Clock is running slow: It is also referred to as losing time i.e. when a normal clock covers 60 minutes, a slower clock will cover less than 60 minutes.

Let's try and solve some examples based on the above information.

Example 1: A watch gains 5 minutes in one hour and was set right at 8 AM. What time will it show at 8PM on the same day?

Solution: A correct clock would have completed 12 hours by 8 pm. But the faster clock actually covers 5 min. extra in one hour. So, it will cover 12 x 5 = 60 minutes extra.
Therefore, when the correct clock would show 8 pm, the faster clock will show 60 minutes extra i.e. 9 pm.

Example 2: A watch loses 5 seconds in one hour and was set right at 7am. What time will it show at 2 pm on the same day?

Solution: A correct clock would have completed 7 hours by 2 pm, whereas the slower clock loses 5 seconds per hour i.e. 5 × 7 = 35 seconds in 7 hours.
Therefore, the slower clock shows 1:59:25 pm.

Example 3: A watch loses 5 minutes every hour and was set right at 6am on a Monday. When will it show the correct time again?

Solution: For the watch to show the correct time again, it should lose 12 hours.
It loses 5 minutes in 1 hour. 
⇒ It loses 1 minute in 12 minutes.
⇒ It will lose 12 hours (or 720 minutes) in 720 × 12 minutes = 8640 minutes = 144 hours = 6 days.
⇒Thus, the clock will show the correct time again at 6am on next Sunday.