An ordinary wall clock with a 12-hour dial is set right at 10 a.m. on a Monday. It gains 4 minutes every day. After how many days will it next show the correct time?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 180
A 12-hour dial shows the same positions every 12 hours. So a fast clock shows the correct time again when its total gain is exactly 12 hours = 720 minutes.
Gain needed \(=12\times60=720\) minutes
Gain in one day \(=4\) minutes
Days needed \(=\displaystyle\frac{720}{4}=180\)
Why the other options are incorrect
Option (1) 90 — Incorrect. After 90 days the gain is only 360 minutes, so the clock is 6 hours ahead.
Option (2) 120 — Incorrect. After 120 days the gain is 480 minutes, so the clock is 8 hours ahead.
Option (3) 360 — Incorrect. This waits for a gain of 24 hours; a 12-hour dial is right again after a gain of only 12 hours.