Lesson 1 of 3 · Gaining / losing clock
Rate error
Clocks and Calendars · for IPMAT Indore, IPMAT Rohtak and JIPMAT · asked in Rohtak 2019
The exam method
- Two clocks. read the true time from one, then the other's reading from its own rate.
- Correct time. from x minutes slow to y minutes fast in T hours, the error changes by x + y; it is zero after x/(x + y) of the interval (JIPMAT 2024: 2 slow, 2.5 fast in 27 h → after 12 h).
Worked examples
Example 4HardRohtak 2019
A clock losing 4 minutes a day is set right at 2 p.m. on 25 February 2008. How many minutes must be added when it shows 9 a.m. on 3 March 2008?
Solution: 9780/359. It shows 163 hours = 9780 minutes; true time is 9780 × 1440/1436, so add 9780 × 4/1436 = 9780/359.
Example 3Easy
Two clocks set right at noon gain 6 and 3 minutes an hour. When the first shows 4:24 p.m., what does the second show?
Solution: 4:12 p.m. The first shows 66 minutes per hour, so 4 true hours have passed; the second shows 4 × 63 = 252 minutes.
Watch out
- Per true hour vs per shown hour: "gains 5 seconds every minute" is per true minute.
Picked from the Gaining / losing clock note for this micro-concept automatically. The whole note: Gaining / losing clock.