Question:
A clock gains 2 minutes every hour. Then the angle traversed by the second hand in one minute is:
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
The correct option is (D): 372°.
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Approach Solution -2
The question describes a clock that gains 2 minutes every hour and asks how large an angle its second hand sweeps through in what the clock itself reads as one minute. Since a normal second hand sweeps 360° in 60 seconds, we can test each option by checking how much faster the second hand must move to produce a 2 minute gain per hour.
- 360°: This is the angle a second hand sweeps in exactly 60 real seconds on a correctly running clock. Since this clock is gaining time, its second hand is moving faster than this, so 360° does not fit here.
- 370°: This would correspond to the clock's face advancing by \( 370/360 \) times the normal rate, which does not match a gain of exactly 2 minutes in every 60 minutes.
- 390°: This would mean the clock's hand is moving noticeably faster than needed for just a 2 minute gain per hour, overshooting the actual rate.
- 372°: A correct clock's minute reading advances by 60 minutes for every 60 real minutes, but this clock advances by \( 60+2=62 \) minutes on its face for every 60 real minutes. So in place of a normal 360° sweep per real minute, the second hand actually sweeps \( 360 \times \frac{62}{60} = 372 \)°, exactly matching this option.
Scaling the normal 360° sweep by the clock's actual 62-minutes-per-60-minutes rate produces exactly 372°, ruling out the other three values.
Therefore, the correct answer is 372°.
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Approach Solution -3
The question describes a clock that runs fast, gaining 2 minutes for every 60 minutes of real time, and asks how large an angle its second hand sweeps through in one real minute. Rather than scaling the full 360° sweep by a ratio, working out just the extra angle caused by the 2-minute gain and adding it to the normal 360° gives the same result from a different direction.
- 360°: This is exactly what the second hand would sweep in one real minute on a perfectly accurate clock, with no extra angle added for any gain, so it does not account for this clock running fast.
- 370°: This would mean an extra 10° added to the base 360°, but the actual extra angle worked out below does not equal 10°.
- 390°: This would mean a considerably larger extra angle of 30° added to the base sweep, more than what this clock's 2-minute-per-hour gain actually produces.
- 372°: Since the clock gains 2 minutes in every 60, it gains \( \frac{2}{60} \) minutes, or 2 seconds, in every real minute. Each second corresponds to \( 6^{\circ} \) of second-hand movement on a correct clock, so this extra 2 seconds adds \( 2 \times 6 = 12^{\circ} \) on top of the normal 360°, giving \( 360+12=372^{\circ} \), matching this option.
Working out just the extra 12° added by the clock's 2-second-per-minute gain and adding it to the standard 360° sweep confirms the same total found by scaling the whole sweep.
Therefore, the correct answer is 372°.
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