Clock puzzles Questions

Q:

How many times in a day, are the hands of a clock in straight line but opposite in direction?

A) 20 B) 22
C) 24 D) 48
 
Answer & Explanation Answer: B) 22

Explanation:

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

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Q:

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

A) 145 B) 150
C) 155 D) 160
 
Answer & Explanation Answer: C) 155

Explanation:

Angle traced by hour hand in 12 hrs = 360º.

Angle traced by hour hand in 5 hrs 10 min.  i.e.,{\color{Black} \frac{31}{6}} hrs {\color{Black} \left ( \frac{360}{12} \times \frac{31}{6}\right )^o}= 155º

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Q:

A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?

A) 2 p.m. on Tuesday B) 2 p.m. on Wednesday
C) 3 p.m. on Thursday D) 1 p.m. on Friday
 
Answer & Explanation Answer: B) 2 p.m. on Wednesday

Explanation:

 

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

{\color{Black} \therefore } The Watch gains {\color{Black} \left ( 2+4\frac{4}{5} \right ) } min.  or {\color{Black} \frac{34}{5} }  min.in 170 hrs.

Now,  min.are gained in 170 hrs.

{\color{Black}\therefore }  2 min.are gained in{\color{Black}\left ( 170\times \frac{5}{34}\times 2 \right ) } hrs=50 hrs

{\color{Black} \therefore } Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday

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Q:

At 3.40, the hour hand and the minute hand of a clock form an angle of:

A) 120 degrees B) 125 degrees
C) 130 degrees D) 135 degrees
 
Answer & Explanation Answer: C) 130 degrees

Explanation:

Angle traced by hour hand in 12 hrs. = 360º.

Angle traced by it in  {\color{Black} \frac{11}{3}} hrs=  {\color{Black} \left ( \frac{360}{12} \times \frac{11}{3}\right )^{o}}={\color{Black}110 ^{o}}

Angle traced by minute hand in 60 min. = 360º.

Angle traced by it in 40 min. ={\color{Black}\left ( \frac{360}{60} \times 40\right )^{o}}={\color{Black}240^{o}}

 {\color{Black} \therefore } Required angle (240 - 110)º = 130º.

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Q:

How many minutes is it until six o’clock if fifty minutes ago it was four times as many minutes past three o’clock?

Answer Twenty-six minutes.
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