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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
