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GATE Mechanical 2023 | GA Question: 4

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We can draw the clock diagram and analyze it.

As of now, the time is $9:15:00$

  • The minute-hand and second-hand of a clock cross each other first time at $9:16$
  • The minute-hand and second-hand of a clock cross each other second time at $9:17$
  • The minute-hand and second-hand of a clock cross each other third time at $9:18$
  • $ \quad \vdots \quad \vdots$
  • The minute-hand and second-hand of a clock cross each other last time at $9:45$

So, $16, 17,18, \dots, 45$

Number of terms $n = ?$

$l = a + (n-1)d,$ here $a=$ first term, $d = $ common difference, $l=$ last term, $n=$ number of terms

Now, $45 = 16 + (n-1)1$

$\Rightarrow 45 = n + 15$

$\Rightarrow n = 30$

Therefore, the minute-hand and second of a clock cross each other $30$ times between $09:15:00$ AM and $09:45:00$ AM on a day

Correct Answer: A

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