Question:medium

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

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“Gains $g$ minutes per hour” $\Rightarrow$ speed factor $=\dfrac{60+g}{60}$. Multiply the usual angular sweep by this factor.
Updated On: Jul 15, 2026
  • $360^\circ$
  • $370^\circ$
  • $390^\circ$
  • $372^\circ$
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The Correct Option is D

Approach Solution - 1

Step 1: The clock gains 2 minutes, that is 120 seconds, every 60 real minutes, that is 3600 real seconds. So its extra speed factor is \( \frac{3600+120}{3600}=\frac{3720}{3600}=\frac{31}{30} \) times normal.

Step 2: A normal second hand completes one full circle, 360 degrees, in one clock minute. Since this clock's minute passes \( \frac{31}{30} \) times faster in real time, the hand covers \( \frac{31}{30} \) full circles in one real minute.

Step 3: The angle swept in one real minute is \( 360 \times \frac{31}{30}=372 \) degrees.
\[ \boxed{372^{\circ}} \]
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Approach Solution -2

A correctly running second hand moves at a steady \( 360^{\circ}/60=6^{\circ} \) per real second. Since this clock's minute passes at \( \tfrac{62}{60}=\tfrac{31}{30} \) times the normal rate, its second hand must move at \( 6 \times \tfrac{31}{30}=6.2^{\circ} \) per real second instead. We can check each option by converting it back to a per-second rate and comparing it to this 6.2 degree figure.

  1. \( 360^{\circ} \): Divided over 60 real seconds, this is \( 360/60=6^{\circ} \) per second, the normal rate, not the faster 6.2 degree rate this clock actually runs at.
  2. \( 370^{\circ} \): This gives \( 370/60 \approx 6.17^{\circ} \) per second, close to but not exactly 6.2 degrees per second.
  3. \( 390^{\circ} \): This gives \( 390/60=6.5^{\circ} \) per second, well above the required 6.2 degree rate.
  4. \( 372^{\circ} \): This gives \( 372/60=6.2^{\circ} \) per second, matching the clock's actual per-second rate exactly.

The clock's second hand moves at exactly 6.2 degrees every real second, which over a full real minute sweeps 372 degrees.

Therefore, the correct answer is \( 372^{\circ} \).

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