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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What is the angle between the hour and minute hand at 3:40?
Answer: B
The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is
\[ \theta = \left| 30H - 5.5M \right| \]
\[ \theta = \left| 30(3) - 5.5(40) \right| = \left| 90 - 220 \right| = 130^{\circ} \]
Taking \( 30H \) as the hour hand's position from 12 automatically includes its drift during the 40 minutes, which is the step most often forgotten.
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Ramesh sets his grandfather’s clock to the right time at 2.00 am on Thursday. But he didn’t know that the clock gains 20s for every 3 hours. What will the clock indicate on Friday night 6.30 pm?
Answer: D
The clock gains 20 seconds in every 3 hours, so first count the hours.
From Thursday 2:00 am to Friday 6:30 pm is
\[ 22 + 18.5 = 40.5 \text{ hours} \]
\[ \text{gain} = 20 \times \frac{40.5}{3} = 20 \times 13.5 = 270 \text{ s} = 4 \text{ min } 30 \text{ s} \]
The clock therefore reads ahead of the true 6:30 pm:
\[ 6{:}30{:}00 + 4{:}30 = 6{:}34{:}30 \text{ pm} \]
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The minute hand and hour hand of a clock meet every 62 minutes. Does the clock gain or lose in 24 hours. And how much does it lose or gain?
Answer: C
In a correct clock the hands coincide every
\[ \frac{720}{11} = 65\tfrac{5}{11} \text{ minutes} \]
Here they coincide every 62 minutes, sooner than they should, so the clock is gaining.
\[ \text{gain per interval} = \frac{720}{11} - 62 = \frac{38}{11} \text{ min} \]
In 1440 minutes there are \( \tfrac{1440}{62} \) such intervals:
\[ \text{gain per day} = \frac{38}{11} \times \frac{1440}{62} = \frac{54720}{682} = 80\tfrac{80}{341} \text{ minutes} \]
Coinciding more often than every \( 65\tfrac{5}{11} \) minutes always means a fast clock; a slower interval, such as 64 minutes, would mean a loss.
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A clock is set right at 5 am the clock loses 16 min in 24 hours. What will be the right time when the clock indicates on 3 pm the 8th day?
Answer: B
Time from 5 am On a day to 3 pm on 8th day = 178 hours
Now 23 hrs 44 min. of this clock = 24 hours of correct clock
365/15 hrs of this clock = 24 hours of correct clock
178 hrs of this clock = (24 × 15/356 × 89) hrs of correct clock
= 180 hrs of correct clock.
So, the correct time is 5 pm.
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How many times in a day, the hands of a clock are straight?
Answer: C
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
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How many times do the hands of a clock coincide in a day ?
Answer: B
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).
The hands overlap about every 65 minutes, not every 60 minutes.
Therefore, The hands coincide 22 times in a day.
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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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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 is started at noon. By 10 minutes past 5, the hour hand has turned through:
Answer: C
The hour hand turns \( 30^{\circ} \) an hour, or \( 0.5^{\circ} \) a minute.
From noon to 5:10 is \( 5\tfrac{1}{6} \) hours:
\[ 5\tfrac{1}{6} \times 30 = 155^{\circ} \]
The extra ten minutes contribute \( 10 \times 0.5 = 5^{\circ} \), which is what lifts the answer above the whole-hour figure.
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