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21. Find the angle between the two hands of a clock of 15 minutes past 4 o'clock.
  A.  37.5°
  B.  38.5°
  C.  36.5°
  D.  35.5°
     
   
View Answer

Shortcut:
To find the angle between hands of clock.
Angle between two hands = 30 x
[
Difference of hours and
minutes / 5
]
+
Minutes / 2

Note: Angle should be less than 90°, we use the following formula,
Angle = 30 x
[
Difference of hours and
minutes / 5
]
−
Minutes / 2

Here, hours = 4, minutes = 15
At 15 minutes past 4, the minute-hand is behind the hour-hand. Hence, using the given formula
Using the above value in the shortcut, we get:
Required angle = 30 x
[
Difference of 4 and
15 / 5
]
+
15 / 2

= 30 + 7.5 = 37.5°

22. Find the angle between the two hands of a clock at 4:30 pm.
  A.  44°
  B.  45°
  C.  50°
  D.  48°
     
   
View Answer

Shortcut:
To find the angle between hands of clock.
Angle between two hands = 30 x
[
Difference of hours and
minutes / 5
]
+
Minutes / 2

Note: Angle should be less than 90°, we use the following formula,
Angle = 30 x
[
Difference of hours and
minutes / 5
]
−
Minutes / 2

Here, hours = 4, minutes = 30
At 4:30 pm the minute hand is ahead of the hour-hand. Therefore, we use the given formula
Required angle = 30 x
[
Difference of 4 and
30 / 5
]
−
30 / 2

= 30 x
[
30 / 5
− 4
]
−
30 / 2

= 30 x 2 − 15 = 45°
Note: Sometimes, time is given in the form of 24 hours instead of 12 hours in order to avoid the confusion of am and pm. For example, 14:20 or 1420 hours. In all such cases when the hour part exceeds 12, we subtract 1200 from it and then solve it. So, 14:20 reduces to 2:20 or 20 minutes past 2.

23. A clock is set right at 8 am. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 pm on the following day?
  A.  26 hours 28 minutes
  B.  28 hours 48 minutes
  C.  29 hours 20 minutes
  D.  25 hours 25 minutes
     
   
View Answer

Time from 8 am on a day to 1pm on the following day is 29 hours.
Now, 24 hours 10 min of this clock are the same as 24 hours of the correct clock.
ie.
145 / 6
hours of this clock = 24 hours of correct clock.
29 hours of this clock =
24x6 / 145
x 29 hours of correct lock = 28 hours 48 min of correct clock.
So, the correct time is 28 hour 48 min after 8 amd or 48 min past 12.

24. A clock is set right at 4 am. The clock loses 20 min in 24 hours. What will be the true time when the clock indicates 3 am. on 4th day?
  A.  4 am
  B.  5 am
  C.  8 am
  D.  3 am
     
   
View Answer

Time from 4 am to 3 am on 3rd day = 24 x 3 − 1 = 71 hours.
Now, 23 hours 40 minute of this clock = 24 hours of correct clock.
or, 23
2 / 3
=
71 / 3
hours of this clock = 24 hours of correct clock.
∴ 71 hours of this clock =
24 x 3 x 71 / 71
= 72 hours of correct clock.
Therefore, the correct time = 3 am + (72 − 71) = 4 am.

25. A watch which gains uniformly is 2 min slow at noon on Monday, and is 4 min 48 seconds fast at 2 pm on the following Monday. When was it correct?
  A.  5 pm on wednesday
  B.  2 pm on wednesday
  C.  3 pm on wednesday
  D.  1 pm on wednesday
     
   
View Answer

Time from Monday noon to 2 pm on following Monday = 7 days 2 hours = 170 hours.
The watch gains
(
2 + 4
4 / 5
)
or,
34 / 5
minutes in 170 hours.
∴ it will gain 2 min in
170 x 5 / 34
x 2 hours
= 50 hours = 2 days 2 hours.
So, the watch is correct 2 days 2 hours after Monday noon i.e, at 2 pm on Wednesday.

26. A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is
  A.  4 pm
  B.  7 pm
  C.  2 pm
  D.  6 pm
     
   
View Answer

Time from 7 am to quarter past 4 = 9 hours 15 min = 555 minutes.
Now,
37 / 12
min of this watch = 3 min of the correct watch.
555 min of this watch =
(
3 x 12 / 37
x 555
)
min
Now,
3x12 / 37
x
555 / 60
hours = 9 hours of the correct watch.
Correct time is 9 hours after 7 am i.e, 4 pm

27. If the hands of a clock coincide every 65 minutes (true time) how much does the clock gain or lose in 24 hours?
  A.  11
9 / 13
min
  B.  12
11 / 9
min
  C.  9
10 / 12
min
  D.  10
10 / 143
min
     
   
View Answer

The minute-hand gains 60 minutes over the hour-hand in
60 x 60 / 55
or 65
5 / 11
minutes.
Therefore, the hands of a correct clock coincide every 65
5 / 11
minutes.
But the hands of the clock mentioned in the question coincide every 65 minutes.
Hence in 65 minutes, the clock gains
5 / 11
minutes.
5 / 11
x
1 / 65
x 60 x 24 = 10
10 / 143
minutes.

28. How many times are the hands of a clock at right angles in a day?
  A.  40 times
  B.  45 times
  C.  44 times
  D.  42 times
     
   
View Answer

In 12 hours, they are at right angles 22 times (because two positions of 3 o'clock and 9 o'clock are common).Therefore, in a day they are at right angles for 44 times.

29. A watch which gains uniformly, is 5 min slow at 8 'o clock in the morning on Sunday, and is 5 min 48 sec fast at 8 pm on following Sunday. When was it correct?
  A.  25 min past 5 pm on Tuesday
  B.  20 min past 7 pm on Wednesday
  C.  15 min past 5 pm on Wednesday
  D.  30 min past 6 pm on Tuesday
     
   
View Answer

Time between the given interval = 180 hours.
The watch gains = 5 + 5
4 / 5
=
54 / 5
minutes in 180 hours
∴ 5 min is gained in
180 x 5 / 54
x 5 minutes. = 83 hours 20 min
= 3 days 11 hours 20 min
∴ it was correct at 20 min past 7 pm on Wednesday.

30. How many times do the hands of a clock point opposite to each other in 12 hours?
  A.  11 times
  B.  9 times
  C.  12 times
  D.  13 times
     
   
View Answer

The hands of a clock point opposite to each other 11 times in every 12 hours (because between 5 and 7, at 6 o'clock only they point poosite to each other).

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