GATE Mechanical 2023 | GA | Question: 4

Question

The minute-hand and second-hand of a clock cross each other ___________ times between $09:15:00$ AM and $09:45:00$ AM on a day.

• A. $30$
• B. $15$
• C. $29$
• D. $31$

Comments

In every min they cross each other.

Answer 1

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

Answer 2

45-16+1=30 times