How much does a watch gain or lose per day, if its hands coincide every 64 minutes?
Answer: D
55 min. spaces are covered in 60 min.
60 min. spaces are covered in (60/55 × 60) min = 65 5/11 min
Loss in 64 min = (65 5/11 - 64) = 16/11 min
Loss in 24 hrs= (16/11 × 1/64 × 24 × 60) min = 32 (8/11) min.
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A watch which gains uniformly in 5 min slows at 8 o? clock in the morning on Sunday and it is 5 min 48 sec fast at 8 pm on the following Sunday. When was it correct?
Answer: C
Time from 8 am on Sunday to 8 pm on following Sunday = 7 days 12 hours
= 180 hours
∴ The watch gains (5 + 29/5) min or 54/5 min in 180 hours.
Now 54/5 minutes are gained in 180 hours.
∴ 5 minutes are gained in [180*(5/54)*5] hour = 83 hr 20 min
= 3 days 11 hours 20 minutes
Watch is correct 3 days 11 hours 20 minutes
after 8 AM of Sunday i.e. 7:20PM on Wednesday.
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An accurate clock shows 10 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 6 o'clock in the evening?
Answer: D
The hour hand sweeps the full \( 360^{\circ} \) in twelve hours, so it turns \( 30^{\circ} \) an hour.
\[ 8 \text{ hours} \times 30^{\circ} = 240^{\circ} \]
Only the hour hand is asked about; the minute hand would have turned \( 8 \times 360^{\circ} \) over the same period.
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How many times do the hands of a clock coincide in a day?
Answer: C
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).
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.
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Ramesh wants to set the clock hands 8 minutes apart between 10 o'clock and 11 o'clock. What would be the time shown in the clock if he does so?
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
\[ \theta = \left| 30H - 5.5M \right| \]
Eight minute-divisions is \( 8 \times 6 = 48^{\circ} \), so with \( H = 10 \):
\[ \left| 300 - 5.5M \right| = 48 \]
\[ 5.5M = 252 \quad\Longrightarrow\quad M = \frac{504}{11} = 45\tfrac{9}{11} \]
\[ 5.5M = 348 \quad\Longrightarrow\quad M = \frac{696}{11} = 63\tfrac{3}{11} \]
The second value exceeds 60, so it falls in the next hour: \( 3\tfrac{3}{11} \) minutes past 11.
The hands coincide at \( 54\tfrac{6}{11} \) minutes past 10, and the two answers sit on either side of that moment.
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If it is 09:20, then what is the angle between the hands of the clock?
Answer: A
At 9 o’ clock, the hour hand is at 270 degrees from the vertical. In 20 minutes,
Hour hand = 270 + 20*(0.5) = 270 + 10 = 280 (The hour hand moves at 0.5 dpm)
Minute hand = 20*(6) = 120 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 280 - 120 = 160 degrees.
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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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At what time between 4 and 5 o' clock will the hands of a clock be at right angle?
Answer: B
At 4 o' clock, the minute hand is 20 minute spaces behind the hour hand.
Now, when the two hands are at right angles, they are fifteen min spaces
apart. So, they are at right angles in following two cases.
Case I ? When the minute hand is 15 min spaces behind the hour hand.
In this case, min hand will have to gain (20-15) = 5 min spaces.
= (60/55)*5 = 60/11
∴ They are at right angle at 60/11 minutes past 4.
Case II ? When the minute hand is 15 minute spaces ahead of the hour hand.
In this case the minute hand will have to gain (20+15) = 35 min spaces.
= (60/55)*35 = 420/11 min
∴ They are at right angles at 420/11 min past 4.
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What will be angle between the two hands of a clock at 10.25 pm?
Answer: C
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
\[ \theta = \left| 30H - 5.5M \right| \]
\[ \theta = \left| 30(10) - 5.5(25) \right| = \left| 300 - 137.5 \right| \]
\[ = 162.5^{\circ} \]
This is the smaller of the two angles; the reflex angle on the other side is \( 360 - 162.5 = 197.5^{\circ} \).
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Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
Answer: A
At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.
Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°
Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5°
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