Multiple choice

Sanju has two watches with a 12-hour cycle. One of these watches gains one minute a day and the other loses 1 and 1/2 minutes per day. If Sanju sets both the watches at the correct time, how long will it be before they again show the correct time together?

  1. 482 days

  2. 290 days

  3. 1440 days

  4. 730 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative gain = 1 - (-1.5) = 2.5 minutes per day. To show the correct time again, the watch must gain or lose a full 12-hour cycle (720 minutes). Days = 720 / 0.5 = 1440 (since the watches are 12-hour cycles, we need to gain 720 minutes).

AI explanation

The first watch gains 1 minute per day and needs to gain 12 hours, or 720 minutes, to show the correct time again, requiring 720 days. The second watch loses 1.5 minutes per day and needs to lose 720 minutes, which takes 480 days. The least common multiple of 720 and 480 is found by factoring them into 144 times 5 and 144 times 3 and 2, making the LCM 1440. The result is 1440 days.

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