Problems on Clocks -Practice Questions - Moderate
22) A clock strikes once
at 12 noon, twice at 1 PM, thrice at 2 PM, and so forth. What will be the total
number of strikes in a day?
a) 78 b) 156 c) 300 d) 312
Answer : B
Explanation :
1 strike at 12 o'clock
2 strikes at 1 o'clock
3 strikes at 2 o'clock
This pattern continues
until 11 o'clock.
So, for the first 12 hours,
the number of strikes is equal to the sum of the first 12 natural numbers:
1+2+3+…+12= 12×(12+1) =78
Since it repeats in the
next 12 hours (from 12 PM to 11 AM ), we need to double this value:
2×78=156
Therefore, the correct
answer is (b) 156
23) Three clocks ring
every 15 minutes, 18 minutes, and 20 minutes, respectively. If the three clocks
ring simultaneously at 4.30 p.m., when will they ring together again?
a)7:05 pm b) 7: 30 p.m. c)
6.45 p.m. d) 5.30 p.m
Answer: B
Explanation:
The clocks will ring
together again after the least common multiple (LCM) of 15, 18, and 20 minutes
= 180 minutes i.e., 3 hours.
After 3 hours from 4:30 p.m.,
the clocks will ring together again at
=> 4.30 + 3 hours. = 7:30
24)
At
what time between 4 and 5’O clock are the two hands of the clock coincide?
a)4.21
9/11 b)4.20 c)4.23 7/11 d)4.22
Answer: A
Explanation :
At
4 o'clock, the hour hand is at 4, and the minute hand is at 12 and there is a
gap of 20 minutes between them.
The
two hands coincide when the minute hand covers this 20-minute gap.
The
time taken by the minute hand to gain 55-minute spaces = 60 minutes
The
time it takes to gain 1 minute space
= 60/55 minutes. = 12/11 minutes
To
gain 20 minutes spaces, the minute hand will take
ð 20 x 12/11 = 240/11 = 21 9/11 minutes.
Therefore, the two hands coincide at 21 9/11 minutes
past 4 o'clock.
25)
At what time between 8 and 9’O clock are the two hands of the clock coincide?
a)
8 : 47 3/11 b)8:
43 7/11 c)8:35 5/11 d)8: 42 8/11
Answer: A
Explanation :
At
8 o'clock, the hour hand is at 8, and the minute hand is at 12 and there is a
gap of 240 minutes between them.
The
two hands coincide when the minute hand covers this 40-minute gap.
The
time taken by the minute hand to gain 55-minute spaces = 60 minutes
The
time it takes to gain 1 minute space
= 60/55 minutes. = 12/11 minutes
To
gain 40 minutes spaces, the minute hand will take
ð 40 x 12/11 = 480/11 = 43 7/11 minutes.
Therefore, the two hands coincide at 8:43 7/11.
26) Find
the time between 8 and 9 o'clock when the two hands of a clock are in the
opposite direction.
a) 8.17
3/11 b) 8.10 c) 8.10 10/11 d) 8.13 7/11
Answer:
C
Explanation:
When the hands are
in opposite directions, they form a 180-degree angle or are 30-minute spaces
apart.
At 8 o'clock, the
minute hand is 40 minute spaces behind the hour hand.
To be in opposite
directions, the minute hand has to gain 10-minute spaces over the hour hand.
The time taken by
the minute hand to gain 55-minute spaces = 60 minutes
The time it takes
for the minute hand to gain 1 minute space = 60/55 minutes = 12/11 minutes
To gain 10 minutes
spaces, the minute hand will take =>
10 x 12/11 = 120/11
= 10 10/11 minutes
Hence, they are in
opposite directions at 10 10/11 minutes past 8 o'clock.
27) Find the time between 3 and 4 o'clock when the
two hands of a clock are in the same straight line but not in the same
direction.
a) 3.36 5/11 b)
3.49 5/11 c) 3.51
9/11 d) 3.39 2/11
Answer: B
Explanation:
When the hands are in opposite
directions, they form a 180-degree angle or are 30-minute spaces apart.
At 3 o'clock, the minute hand
is 15 minute spaces behind the hour hand.
To be in opposite directions,
the minute hand has to gain 45-minute spaces over the hour hand.
The time taken by the minute
hand to gain 55-minute spaces = 60 minutes
The time it takes for the
minute hand to gain 1 minute space = 60/55 minutes = 12/11 minutes
To gain 45 minutes spaces, the
minute hand will take:
45 x 12/11 = 49 1/11 minutes
Hence, they are in opposite
directions at 3: 49 5/11
28) At what time between 5 and 6’O clock will the
two hands of a clock be at the right angle?
a)
5.43 7/11 b)5.10 10/11
c)5.12 8/11 d) a and b both
Answer : D
Explanation :
Between
5 and 6 o'clock, the two coincide at 5: 25
To
have a right angle between them, the two hands should be 15-minute spaces
apart.
(i)
The minute hand has to be 15 minute spaces behind the hour hand, or
(ii)
the minute hand has to be 15-minute spaces ahead of the hour hand.
Case
1: The minute hand is 15 minute spaces behind the hour hand, the minute hand
must gain (25 - 15) = 10 minute spaces over the hour hand.
ð 10 x 12/11
= 120/11 = 10 10/11 minutes
Thus,
the two hands form a right angle at 10 10/11 minutes past 5 o'clock.
Case
2: The minute hand is 15-minute spaces ahead of the hour hand, the minute hand
has to gain (25 + 15) = 40-minute spaces.
To
gain 40 minute spaces, the minute hand takes => 40 x 12/11 = 480/11 = 43
7/11
Therefore,
the two hands will be at a right angle at 43 7/11 minutes past 5 o'clock.
The
correct answers are options (a) 5.43 7/11 and (b) 5.10 10/11.
29) At what time between 7 and 8 o'clock will the two hands of a
clock be at a right angle?
a) 7.54 6/11 b) 7.21 9/11 c) 7.42 7/11 d) b and c both
Answer: D
Explanation:
Between 7 and 8 o'clock, the two hands
coincide at 7:35.
To have a right angle between them, the two
hands should be 15 minute spaces apart.
(i) The minute hand has to be 15 minute
spaces behind the hour hand, or
(ii) The minute hand has to be 15 minute
spaces ahead of the hour hand.
Case 1: The minute hand is 15 minute spaces
behind the hour hand.
The minute hand must gain (35 - 15) = 20
minute spaces over the hour hand.
=> 20 x 12/11 = 240/11 = 21 9/11 minutes
Thus, the two hands form a right angle at 21
9/11 minutes past 7 o'clock.
Case 2: The minute hand is 15 minute spaces
ahead of the hour hand. The minute hand has to gain (35 + 15) = 50 minute
spaces.
To gain 50 minute spaces, the minute hand takes
=> 50 x 12/11 = 600/11 = 54 6/11
Therefore, the two hands will be at a right
angle at 54 6/11 minutes past 7 o'clock.
The correct answers are options (a) 7.54 6/11
and (d) 7.21 9/11.
30) At what time between 4 and 5 are the hands 9
minutes spaces apart?
a)
4 19 7/11 and 4.22
b)4.21
7/11 and 4.24
c)
4. 12 and 4:31
d)
4.18 9/11 and 4.24 2/11
Answer
: A
Explanation
:
Between
4 and 5 o'clock, the two hands of the clock are 20 minute spaces apart at 4
o'clock.
Case
1:
If
the minute hand is 2 minutes behind the hour hand, it has to gain (20 - 9) = 11
minute spaces.
The
time the minute hand takes to gain 1 minute space =
60/55 minutes. = 12/11 minutes
To
gain 11 minute spaces > 11 × 12/11 =
12 minutes.
Therefore,
the two hands will be 2 minutes apart at 4 : 12
Case
2:
If
the minute hand is 2 minutes ahead of the hour hand, it has to gain (20 + 9) =
29 minute spaces.
To
gain 29 minute spaces , the minute hand will take => 29 × 12/11 = 31 7/11 minutes.
The correct answer is option (c) 4.12 and 4.31 7/11 minutes
31) At what time between 7 and 8 o'clock will the two hands of a
clock be 60 degrees apart?
a) 7:27 3/11 and 7 49 1/11 b)
7.50 5/11 and 7.59
c) 7.38 10/11 and 7.48 2/11 d) None of the above
Answer: A
Explanation:
60 degrees = 60/6 = 10 minute spaces
Between 7 and 8 o'clock, the two hands of the
clock are 35-minute spaces apart at 9 o'clock.
Case 1:
If the minute hand is 10 minutes behind the
hour hand, it has to gain (35 - 10) = 25 minute spaces.
The time the minute hand takes to gain 1
minute space = 60/55 minutes = 12/11 minutes.
To gain 25 minute spaces > 25 × 12/11 = 27
3/11 minutes.
Therefore, the two hands will be 10 minutes
apart at 7:27 3/11.
Case 2:
If the minute hand is 10 minutes ahead of the
hour hand, it has to gain (35 + 10) = 45 minute spaces.
To gain 45 minute spaces, the minute hand
will take => 45 × 12/11 = 49 1/11 minutes.
The correct answer is option (d) 7.27 3/11
and 7 49 1/11.
