Two wall clocks with 12-hour dials are both set right at 12 noon. The first clock gains 2 minutes a day and the second clock loses 3 minutes a day. After how many days will the two clocks next show the same time?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 144
The two clocks show the same time again when the gap between them becomes exactly 12 hours = 720 minutes, because a 12-hour dial repeats its positions every 12 hours. One clock runs ahead and the other falls behind, so the gap grows by the sum of the two daily errors.
Gap made in one day \(=2+3=5\) minutes
Gap needed \(=12\times60=720\) minutes
Days needed \(=\displaystyle\frac{720}{5}=144\)
Why the other options are incorrect
Option (1) 240 — Incorrect. This is when the second clock alone is right again (\(720\div3\)), ignoring the first clock’s gain.
Option (3) 288 — Incorrect. This waits for a gap of 24 hours (\(1440\div5\)); 12 hours is enough on a 12-hour dial.
Option (4) 360 — Incorrect. This is when the first clock alone is right again (\(720\div2\)).