Question:medium

A clock gains 2 minutes every hour. Then the angle traversed by the second hand in one minute is:

Updated On: Jul 15, 2026
  • 360°
  • 370°
  • 390°
  • 372°
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The Correct Option is D

Approach Solution - 1

Step 1: Compare the clock's face reading to real time.
The clock gains 2 minutes every hour, so while 60 real minutes pass, the clock's face shows \( 60+2=62 \) minutes.

Step 2: Find the scale factor between clock time and real time.
For every 60 real minutes, the clock reads 62 minutes, a scale factor of \( \frac{62}{60} \).

Step 3: Apply this scale factor to the second hand's normal sweep.
On a correct clock, the second hand sweeps \( 360 \)° in one real minute. On this fast clock, the second hand sweeps: \[ 360 \times \frac{62}{60} = 372 \] degrees in one real minute.

Step 4: Final Answer.
Since the clock runs fast by a factor of 62/60, its second hand covers 372° instead of the usual 360° in each real minute. \[ \boxed{372^{\circ}} \]
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Approach Solution -2

Another way to find the second hand's sweep is to work out how many full revolutions it makes over an entire real hour, given the clock's gain, and then divide that total angle by 60 to get the sweep for a single real minute.

  1. 360°: Over one real hour, a correct second hand would complete exactly 60 revolutions of 360° each, giving 360° per real minute, but this ignores the extra revolutions caused by the clock's gain.
  2. 370°: This would correspond to the second hand completing slightly more than 61 revolutions in a real hour, which does not match the gain given in the question.
  3. 390°: This would correspond to completing 65 revolutions in a real hour, well beyond what a 2-minute gain per hour actually produces.
  4. 372°: Since the clock gains 2 minutes every 60 real minutes, its face advances by 62 minutes in that same real hour, meaning the second hand completes 62 full revolutions of 360° each, a total of \( 62\times360=22320^{\circ} \), over 60 real minutes. Dividing this total by 60 gives \( 22320\div60=372^{\circ} \) per real minute, matching this option.

Counting the full 62 revolutions the second hand makes over a real hour and dividing by 60 gives the same 372° per real minute found by other approaches.

Therefore, the correct answer is 372°.

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