TIFR CSE 2010 | Part A | Question: 2

Question

The hour hand and the minute hands of a clock meet at noon and again at mid-night. In between they meet $N$ times, where $N$ is.:

• A. $6$
• B. $11$
• C. $12$
• D. $13$
• E. None of the above

Answer 1

Let $\delta$ be the difference in minutes between hour and minute hand at $1:05$. So, the meeting times are

$1:05 + \delta$

$2:10 +2 \delta$

$3:15 + 3\delta$

$4:20 + 4\delta$

$5:25 + 5\delta$

$6:30 + 6\delta$

$7:35 +7 \delta$

$8:40 +8 \delta$

$9:45 + 9\delta$

$10:50 +10 \delta$

$11:55 +11 \delta$

We have $11\delta =5$

$\implies \delta = \dfrac{5}{11}$

minutes as the meeting time is $0:00$. So, we have $N=10.$

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Alternatively,

Speed of minute hand = $360$ degrees per $60$ minutes = $6$ degrees per minute.

Speed of hour hand = $360$ degree per $12 * 60$ minutes = $0.5$ degree per minute. 

For first meeting, distance traveled by minute hand = $360$ $+$ distance traveled by hour hand

Let, $x$ be the minutes after which the hands intersect.

So, $6x = 360 + 0.5 x $

$\implies 5.5x = 360 $

$\implies x = \dfrac{720}{11}$ 

In $12$ hours we have $12 \times 60$ minutes. 

So, no. of intersections $= \dfrac {12 \times 60}{720/11} = 11$. 

But the last intersection is at midnight and must be excluded as per given question. So, $N=10$.

Correct Answer: $E$

Comments

great job Arjun sir

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how 11 do/5? Please explain

Answer 2

ANS : e)

10

between 11 and 1 , hour hand and minute hand meets only one time at 12:00 , we need to exclude this , as they asked in between noon and midnight.

1-2-3-4-5-6-7-8-9-10-11

between every hour they meet once

Comments

ya , u r correct I think none of the above shud be correct..

Answer 3

11 Times.

Comments

digvijay sir last intersection will be excluded as it occur at midnight

Answer 4

In a hour, minute and hour hands meet exactly once.

Total: 12Hr => 12 meets

They asked to calculate for in between 12 noon and 12 midnight,

At 12 noon: 1 meet

At 12 midnight: 1 meet
Excluding above gives 12-2= 10 meets.

Option: e) None

Comments

Good, practical approach. (y)