I have two watches with a 12 hour cycle. One of them gains one minute a day and the other loses $1 \frac{1}{2}$ minutes per day. If I set them both at the correct time, how long will it be before they again tell the correct time together?
(a)288 days
(b)480 days
(c)720 days
(d)1440 days
Answer
Answer (as printed): D
Explanation
Clearly, the first watch will show the correct time when it has gained 12 hours i.e., $(12 \times 60)=720 \mathrm{min}$ and the secon watch will show the correct time when it has lost 720 min. Time taken by first watch to gain $720 \mathrm{min}=720$ days. Time taken by second watch to gain 720 min $=\left(720 \div 1 \frac{1}{2}\right)$ days $=\left(720 \times \frac{2}{3}\right.$ days $)=480$ days . So the first watch shows correct time after every 720 days and the second wach after every 480 days. ∴ Time after which both the clocks will together tell the correct time = L.C.M. of 720 and $480=1440$ days.