Start here · the first lesson of Gaining / losing clock
Gaining / losing clock
Clocks and Calendars · for IPMAT Indore, IPMAT Rohtak and JIPMAT
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The idea
A faulty clock runs at a steady wrong rate. Every question reduces to a proportion between shown time and true time, or to the moment when a steadily changing error passes zero. Rohtak 2019 and JIPMAT 2024-2025 each set one.
Textbook vs exam method
Textbook method
Find how many minutes the clock shows for a fixed number of true minutes. Convert the shown interval into true time (or the reverse) with that ratio; the difference is the error.
Exam method
- 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).
- Shown to true. a clock that gains 15 minutes in 20 hours shows 1215 minutes per 1200 true minutes.
- Two clocks. read the true time from one, then the other's reading from its own rate.
- Leap years. count 29 February when the interval crosses it (Rohtak 2019: 163 hours from 25 Feb to 3 March 2008).