If the minute hand of a clock has moved 300º, how many degrees has the hour hand moved?
Answer: A
The speed of hour hand is 0.5 dpm (Degree per Minute)
And the speed of minute hand is 6 dpm.
So, 300 degree traverse by minute hand in 300/6 = 50 Minutes.
Thus, angle moved by the hour hand in 50 minutes is 50/0.5 = 25° degrees.
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A clock when seen in a mirror shows 11:25. What is the correct time?
Answer: B
A mirror reverses the dial, so a reading of \( T \) appears as \( 12{:}00 - T \) (or \( 11{:}60 - T \), which is easier to subtract).
\[ 11{:}60 - 11{:}25 = 0{:}35 \quad\Longrightarrow\quad 12{:}35 \]
Checking: 12:35 seen in a mirror does show 11:25, since the two are equally far either side of the 12.
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If real time is 12:10 then what will be mirror image of that clock?
Answer: B
A mirror reverses the dial, so a reading of \( T \) appears as \( 12{:}00 - T \) (or \( 11{:}60 - T \), which is easier to subtract).
\[ 11{:}60 - 12{:}10 \]
Treating 12:10 as 0:10:
\[ 11{:}60 - 0{:}10 = 11{:}50 \]
So the mirror shows 11:50.
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A watch gain 8 seconds in 4 minutes and was set right at 4 AM. What time will it show at 11 PM on the same day?
Answer: C
8 Seconds in 4 Minutes mean 120 Seconds (or 2 Minutes) in one hour.
From 4AM to 11PM (on the same day) = 19 hours
So, total seconds gain in 19 hours = 19 X 120 (Seconds gain per hour) = 2280 Seconds.
Now, 2280 Seconds = 38 Minutes (i.e. 2280/19 = 38)
Thus incorrect clock will show 11:38PM at 11PM.
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A clock loses 5 minutes every hour and was set right at 11AM on a Monday. When will it show the correct time again?
Answer: A
As mentioned in Key Point O, faulty clock will show correct time when it loses or gains 12 Hours.
In the given problem, clock loses 5 Minutes in an hour. So, 1 Minute lost in every 12 minutes (60 minutes / 5 minutes = 12 minutes).
Now, for losing 12 hours i.e. 720 Minutes(12 X 60 = 720) it will take 720 X 12 = 8640 Minutes = 144 Hours = 6 Days.
So, Clock will show correct time after 6 days from 11AM Monday.
Thus, Answer is 11AM on Sunday.
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My watch, which gains uniformly, is 2 min and show at noon on Sunday, and is 4 min 48 seconds fast at 2PM on the following Sunday when was it correct?
Answer: D
At noon on Sunday watch gains 2 Minutes.
And at 2PM on following Sunday it is 4 Minutes 48 Seconds fast.
So, it gains 6 Minutes 48 Seconds i.e. 2 Minutes + 4 Minutes 48 Seconds (total 408 Seconds) in 170 Hours (Hours from Sunday Noon (12PM) to following Sunday 2PM)
Therefore, watch gains 120 Seconds (2 Minutes) in 170*120/408 = 50 Hours
50 Hours = 2 Days 2 Hours
Thus, Watch was correct after 2 days 2 hours from Sunday noon that is Tuesday 2PM.
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How many times in a day, are the hands of a clock in straight line but opposite in direction.
Answer: B
The hands are opposite once in every hour except between 5 and 6 o'clock, where the opposition falls exactly at 6 and is shared with the next hour.
\[ 11 \text{ times in 12 hours} \times 2 = 22 \text{ times in a day} \]
The count matches the 22 coincidences, since the hands are opposite exactly once between successive meetings.
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How many times in a day, are the hands of the clock straight?
Answer: B
"Straight" covers both cases: the hands together and the hands opposite.
\[ 22 \text{ coincidences} + 22 \text{ oppositions} = 44 \text{ times a day} \]
Coincidentally this equals the number of right angles, but for a different reason.
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How many times do the hands of a clock are in perpendicular to each other in a day?
Answer: C
In each twelve-hour period the hands are at right angles 22 times - twice in most hours, but the crossings near 3 and 9 o'clock overlap so that two are lost.
\[ 22 \times 2 = 44 \text{ times in 24 hours} \]
The count is not 48, because between 2–3 and 3–4 (and again around 9) one right angle is shared rather than occurring twice.
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In a minute, how many degrees hour hand traverses?
Answer: A
The hour hand covers \( 360^{\circ} \) in twelve hours:
\[ \frac{360}{12} = 30^{\circ} \text{ per hour} \]
\[ \frac{30}{60} = 0.5^{\circ} \text{ per minute} \]
The minute hand, by contrast, does \( 6^{\circ} \) a minute - twelve times as fast.
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