Home ≫ Arithmetic Aptitute ≫ Clocks ≫ Page 2
11. Find at what time between 2 and 3 o'clock will the hands of a clock be in the same straight line but not together.
  A.  44
8 / 11
min past 5
  B.  44
5 / 10
min past 7
  C.  43
7 / 11
min past 9
  D.  42
8 / 11
min past 8
     
   
View Answer

Shortcut:
Between z and (z + 1) o'clock, the two hands are in the same straight line
Case I: (a) When they are in opposite directions i.e, 30 minutes spaces apart, at (5z − 30)
(
12 / 11
)
minutes past z. [where z > 6]
(b) When z< 6, the above formula will become as (5z + 30)
(
12 / 11
)
minutes past z.
Note: At 6 o'clock two hands will be in opposite direction.
Case II: When they coincide (or come together), i.e 0 minutes spaces apart at 5z x
12 / 11
minutes past z.
Here, z = 2
Using the above value in the shortcut, we get:
Required value = (5 x 2 + 30) x
12 / 11
minutes past 2
= 40 x
12 / 11
minutes past 2
=
480 / 11
minutes past 2
= 43
7 / 11
minutes past 2.

12. At what time between 5 and 6 are the hands of a clock 3 minute apart?
  A.  21 min past 9
  B.  20 min past 5
  C.  23 min past 8
  D.  24 min past 6
     
   
View Answer

Shortcut:
Between z and (z + 1) o'clock, the two hands will be 't' minutes apart at (5z ± t)
12 / 11
minutes past z.
Here, z = 5, t = 3
Using the above value in the shortcut, we get:
Required value = (5 x 5 ± 3) x
(
12 / 11
)

= (25 − 3) x
12 / 11
or (25 + 3) x
12 / 11

= 22 x
12 / 11
or 28 x
12 / 11

=
22 x 12 / 11
or
28 x 12 / 11

=
264 / 11
or
336 / 11

= 24 or 30
6 / 11

Hence, they will be 3 minutes apart at 24 minutes past 5.

13. At what time between 3 and 4 is the minute-hand 7 minutes ahead of the hour-hand?
  A.  24 minutes past 7
  B.  22 minutes past 5
  C.  21 minutes past 3
  D.  20 minutes past 8
     
   
View Answer

Shortcut:
Between z and (z + 1) o'clock, the two hands will be 't' minutes apart at (5z ± t)
12 / 11
minutes past z.
Here, z = 3, t = 7
Using the above value in the shortcut, we get:
Required value = (5 x 3 ± 7) x
(
12 / 11
)

= (15 − 7) x
12 / 11
or (15 + 7) x
12 / 11

= 8 x
12 / 11
or 22 x
12 / 11

=
8 x 12 / 11
or
22 x 12 / 11

=
96 / 11
or
264 / 11

= 8
8 / 11
or 24
Hence, they will be 7 minutes ahead at 24 minutes past 7.

14. At what time between 3 and 4 is the minute-hand 4 minutes behind the hour-hand?
  A.  11 min past 5
  B.  12 min past 3
  C.  13 min past 5
  D.  10 min past 5
     
   
View Answer

Shortcut:
Between z and (z + 1) o'clock, the two hands will be 't' minutes apart at (5z ± t)
12 / 11
minutes past z.
Here, z = 3, t = 4
Using the above value in the shortcut, we get:
Required value = (5 x 3 ± 4) x
(
12 / 11
)

= (15 − 4) x
12 / 11
or (15 + 4) x
12 / 11

= 11 x
12 / 11
or 19 x
12 / 11

= 12 or
19 x 12 / 11

= 12 or
228 / 11

= 12 or 20
8 / 11

Hence, they will be 4 minutes behind the hour-hand at 12 minutes past 3.

15. The minute hand of a clock overtakes the hour hand at intervals of 63 minutes of correct time. How much a day does the clock lose or gain?
  A.  Loss of 53
8 / 71
min
  B.  Gain of 55
9 / 74
min
  C.  Gain of 56
6 / 75
min
  D.  Gain of 56
8 / 77
min
     
   
View Answer

Shortcut:
The minute hand of a clock overtakes the hour hand at certin interals (given in minutes) of correct time. The clock lose or gain in a day is given by
[
720 / 11
− given interval in minutes
]
x
[
60 x 24 / given interval in minutes
]
according as the sign is +ve or − ve.
Here, given interval in minutes = 63
Using the above value in the shortcut, we get:
Required value =
[
720 / 11
− 63
]
x
[
60 x 24 / 63
]

=
27 / 11
x
60 x 24 / 63

=
27 / 11
x
20 x 8 / 7

=
4320 / 77
= 56
8 / 77

Hence, the +ve sign shows that there is a gain of 56
8 / 77
minutes.

16. How much does a watch gain or lose per day, if its hands coincide every 64 minutes?
  A.  32
8 / 11
minutes
  B.  33
7 / 9
minutes
  C.  31
5 / 11
minutes
  D.  33
9 / 8
minutes
     
   
View Answer

Shortcut:
The minute hand of a clock overtakes the hour hand at certin interals (given in minutes) of correct time. The clock lose or gain in a day is given by
[
720 / 11
− given interval in minutes
]
x
[
60 x 24 / given interval in minutes
]
according as the sign is +ve or − ve.
Here, given interval in minutes = 64
Using the above value in the shortcut, we get:
Required value =
[
720 / 11
− 64
]
x
[
60 x 24 / 64
]

=
720 − 704 / 11
x
15 x 3 / 2

=
16 / 11
x
45 / 2
=
8 x 45 / 11
=
360 / 11
= 32
8 / 11

Hence, the +ve sign shows that there is a gain of 32
8 / 11
minutes.

17. At what angle are the hands of a clock inclined at 25 minutes past 5?
  A.  11.3°
  B.  13.5°
  C.  12.5°
  D.  11.8°
     
   
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 = 5, minutes = 25
Using the above value in the shortcut, we get:
Required angle = 30 x
[
Difference of 5 and
25 / 5
]
+
25 / 2

= 30 x 0 + 12.5 = 12.5°
Hence, at 12.5° the hands of a clock will be inclined.

18. At what angle the hands of a clock are inclined at 15 minutes past 5?
  A.  68.5°
  B.  67.5°
  C.  66.5°
  D.  65.5°
     
   
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 = 5, minutes = 15
Using the above value in the shortcut, we get:
Required angle = 30 x
[
Difference of 5 and
15 / 5
]
+
15 / 2

= 30 x 2 + 7.5 = 67.5°
Hence, at 67.5° the hands of a clock will be inclined.

19. At what angle are the hands of a clock inclined at 55 minutes past 8?
  A.  60.5°
  B.  61.5°
  C.  63.5°
  D.  62.5°
     
   
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 = 8, minutes = 55
Using the above value in the shortcut, we get:
Required angle = 30 x
[
Difference of 8 and
55 / 5
]
+
55 / 2

= 30 x 3 + 27.5 = 117.5°
But it is not correct.
If we think carefully we find that the angle should be less than 90°.
In this case, the formula differs and is given below as
Angle = 30 x
[
Difference of 8 and
55 / 5
]
−
55 / 2

= 30 x 3 − 27.5 = 62.5°
Hence, at 62.5° the hands of a clock will be inclined.
Note: The two types of formula work in two different cases.
(1) When hour hand is ahead of the minute hand ( like, when the minute hand is at r, the hour hand should be after 4, i.e., between 4 & 5, 5 & 6 and so on...) We use the formula.
30 x
[
Difference of hours and
minutes / 5
]
+
minutes / 2

(2) When the hour hand is behind the minute hand, we use the formula:
30 x
[
Difference of hours and
minutes / 5
]
−
minutes / 2

20. Find the time between 3 and 4 o'clock when the angle between the hands of a watch is one-third of a right angle.
  A.  13
7 / 9
min past 3
  B.  11
13 / 10
min past 3
  C.  10
10 / 11
min past 3
  D.  12
11 / 10
min past 3
     
   
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 = 3, minutes = M
Using the above value in the shortcut, we get:
Required angle = 30 x
[
Difference of 3 and
M / 5
]
+
M / 2

30 = 30 x
[
3 −
M / 5
]
+
M / 2

or, 30 = 6(15 − M) +
M / 2

or, 30 =
12(15 − M) + M / 2


or, 60 = 180 − 12M + M
or, 60 = 180 − 11M
or, 11M = 180 − 60
or, 11M = 120
or, M =
120 / 11

or, M = 10
10 / 11

Hence, at 10
10 / 11
minutes past 3, the angle between the hands of a watch is one-third of a right angle.

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .