Multiple choice

A clock gains five minutes every hour. What will be the angle traversed by the second hand in one minute?

  1. 360°

  2. 390°

  3. 360.5°

  4. 380°
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A normal clock second hand moves 360 degrees in 60 seconds (1 minute). If the clock gains 5 minutes every hour, it gains 5/60 = 1/12 minutes every minute. The second hand covers 360 degrees in 60 seconds, plus the gain of 5/60 minutes (which is 5 seconds). 360 + (5/60 * 360) = 360 + 30 = 390 degrees.

AI explanation

Because the faulty clock gains 5 minutes every hour, its second hand completes 65 full rotations instead of the normal 60 rotations in that same actual hour. Therefore, the ratio of faulty rotations to true minutes is 65 divided by 60, which simplifies to 13 divided by 12. Multiplying the standard 360 degree rotation by this 13 divided by 12 ratio yields 390 degrees traversed by the second hand in one true minute.

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