SSC Questions on Clock:
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Question 1: At what time between 11 O’Clock and 12 O’Clock, will the minute hand and hour hand of the clock coincide with each other?
a) $11:54\dfrac{9}{11}$
b) $11:01\dfrac{6}{11}$
c) $11:56$
d) None of these
Question 2: What is the obtuse angle formed by the hands of a clock when the time in the clock is 2:30?
a) $95^\circ$
b) $120^\circ$
c) $105^\circ$
d) $165^\circ$
Question 3: A watch loses 5 minutes every hour and was set right at 6 a.m. on a Monday. When will it
show the correct time again?
a) 6 a.m. on next Sunday
b) 3 a.m. on next Monday
c) 3 a.m. on next Sunday
d) 6 a.m. on next Monday
Question 4: An alarm was set at 11 AM on Monday on a clock that was set correctly at 1 AM on Sunday, but the clock started gaining 20 seconds every 24 hours. What was the actual time when the alarm went off?
a) 10:31:40 AM
b) 10:51:20 AM
c) 10:30:00 AM
d) 11:30:00 AM
Question 5: What is the angle between the two hands of a clock when the time shown by the clock is 8 p.m.?(in degrees)
a) 240
b) 120
c) 60
d) 50
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Question 6: How many times in a week does both the hands of the clock will coincide with each other?
a) 84
b) 160
c) 56
d) 154
Question 7: If the hour hand of a clock moves by $18^\circ$ then by how many degrees does the minute hand move during the same time?
a) 168
b) 216
c) 276
d) 196
Question 8: In a week, how many times are the hands of clock at right angles with each other?
a) 308
b) 44
c) 24
d) 154
Question 9: At what time between 4 O’Clock and 5 O’Clock, will the minute hand and hour hand of the clock coincide with each other?
a) $04:21\dfrac{9}{11}$
b) $04:20\dfrac{6}{11}$
c) $04:22$
d) $04:21$
Question 10: A clock is found to be slow by 5 minutes at 8 AM on Sunday. It started gaining time and was found to be 5 minutes fast at 8 PM on Monday. When was it correct?
a) 8 AM, Monday
b) 2 AM, Monday
c) 6 AM, Monday
d) 8 PM, Monday
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Answers & Solutions:
1) Answer (D)
Angle between two hands $= \dfrac{11}{2}M – 30H$ where H is hours and M is Minutes
Here, H = 11 and Angle = $0^\circ$
$0^\circ = \dfrac{11}{2}M – 30\times11$
⇒ $\dfrac{11}{2}M = 330$
⇒ $M = \dfrac{660}{11} = 60$
Hence, the required time = $11:60$ which is $12:00$
Hence, Between 11 O’Clock and 12 O’Clock, the minute hand and hour hand will not coincide with each other.
2) Answer (C)
Angle between the hands of a clock is given by the formula $\dfrac{11}{2}H – 30M$ or $30M – \dfrac{11}{2}H$ where H is hours and M is minutes.
Here, Given time = 02 : 30, H = 2 and M = 30.
Angle = $\dfrac{11}{2} \times 30 – 30 \times 2 = 165 – 60 – 105^\circ$
3) Answer (A)
For the watch to show the correct time again, it should lose 12 hours.
It loses 5 minutes in 1 hour.
⇒ It loses 1 minute in 12 minutes.
⇒ It will lose 12 hours (or 720 minutes) in 720 × 12 minutes = 8640 minutes = 144 hours = 6 days.
⇒Thus, the clock will show the correct time again at 6am on next Sunday.
So , the answer would be option a) 6 a.m. on next Sunday.
4) Answer (E)
Total time between sunday at 1 AM to monday at 11 AM =24hours + 10hours = 34 hours
Now total gain in seconds in 34 hours = $\frac{20}{24}$×34= $\frac{85}{3}$
The actual time at which alarm went off is
=10:59:(60-$\frac{85}{3}$)
=10:59:$\frac{95}{3}$
=10:59:32
5) Answer (B)
The total angle in a clock is 360°.
The minute hand covers this 360° in 60 minutes. Thus ,for every minute it covers 6°.
The hour hand covers this 360° in 12 hour. Thus ,for every hour it covers 30°.
So, in 8 hour ,the hour hand will cover $8\times30°=240°.$
So, the difference between hour hand and minute hand at 8 p.m will be = $\left(360°-240°\right)=120°.$
So, option B is correct .
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6) Answer (D)
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.
So, both the hands coincide with each other for 22 times in a day.
Now,
For 1 day = 22 times.
For 1 week = 22 * 7
= > 154 times.
7) Answer (B)
The hour hand of a clock moves by 30 deg when the minute had moved through 360 deg. Hence if the hour hand moves 18 deg, then the minute hand moves by $\frac{360\times18}{30}$ = 216 deg
8) Answer (A)
If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In a 24 hour day you get $2\times 22= 44$
so in weekthere are 7 days
so,
$7\times 44= 308 times$
9) Answer (A)
Angle between two hands $= \dfrac{11}{2}M – 30H$ where H is hours and M is Minutes
Here, H = 4 and Angle = $0^\circ$
$0^\circ = \dfrac{11}{2}M – 30\times4$
⇒ $\dfrac{11}{2}M = 120$
⇒ $M = \dfrac{240}{11} = 21\dfrac{9}{11}$
Hence, the required time = $04:21\dfrac{9}{11}$
10) Answer (B)
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