GATE 2024 XH5 (Psychology) – Question 5
On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
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Correct answer: (C) 50
Explanation
The second hand overtakes the minute hand 59 times an hour, first at 12:00:00 and then every $\frac{3600}{59} \approx 61.02$ seconds. The window 12:05:00 to 12:55:00 is from 300 s to 3300 s. The multiples of 61.02 that fall in it run from $5 \times 61.02 = 305.1$ to $54 \times 61.02 = 3294.9$, which is 50 crossings.