Problems on Clocks - Difficult Questions
32) Four clocks ring every 10 minutes, 14 minutes, 21 minutes, and 42 minutes respectively. If
the three clocks ring simultaneously at 12.30 p.m., when will they ring
together again for the last time in the day?
a) 11:45 p.m
b) 7:30 p.m
c) 11:00 p.m
d) 10.45 p.m
Answer:
Explanation:
The clocks will ring together again after the
least common multiple (LCM) of 10, 14, and 21 minutes
LCM of 10, 14, 21 and 42 = 210 minutes.
210
minutes = 3 hours 30 minutes
After 210 minutes from 12:30 p.m., the clocks
will ring together again at => 12:30 + 3 hours 30 minutes
12:30 + 3 hours 30 minutes = 4 p.m
Again
(4 p.m + 3 hours 30 minutes) = 7.30
Again
( 7.30 p.m + 3 hours 30 minutes) =11 p.m
Therefore, the last time in the day when the
clocks will ring together is 11 p.m.
33) A wall clock loses 2% time during the first 5
days and then gains 3.5% time during the next 5 days. The clock is set correctly
at midnight on Monday. What time will the clock show precisely after ten days
from the time it is set to correct?
A) 1:22:48 a.m B) 11:30:15 p.m C) 12:45 p.m D)
2:10:36 p.m
Explanation:
Number of hours in 5 days = (5 x 24) = 120 hours
During the first 5 days, the clock gains 2% time, and during the
next 5 days, it loses 3.5%.
Total gain or lose = (3.5% - 2%) = 1.5% gain
The total time gained is = 1.5% of 120 hours = 1.8 hours.
1.8 hours = 1 hour 48 minutes
After 10 days, the clock will show the time => (12 a.m + 1 hour
48 minutes)
= 1.48 a.m
Therefore, the correct answer is A) 1:48 a.m.
34) Two clocks
A and B take 35 seconds and 42
seconds respectively to strike at 8 O’ clock. What is the interval of time
between the 7th stroke of the first clock and the 8th stroke of the second
clock when both clocks strike at 12 O’clock?
a) 5 seconds b)6
seconds c)12 seconds d)10.5 seconds
Explanation:
To strike at 8 O’clock, the number of intervals will be 7.
Clock A: The time interval between two successive strokes = 35/7 =
5 seconds.
Clock B: The time interval between two successive strokes = 42/7 =
6 seconds.
When both the clocks strike at 12 O'clock:
For the 7th stroke or 6 intervals, clock A takes = 6 x 5 = 30
seconds.
For the 8th stroke or 7 intervals, clock B takes = 7 x 6 = 42
seconds.
The interval of time between the 7th stroke of the first clock and
the 8th stroke of the second clock is given by subtracting the time taken by
clock A from the time taken by clock B:
Required time interval = (42 seconds – 30 seconds) = 12 seconds.
35) In a particular time interval, the hour hand makes the angle 650. Then by how many degrees are the initial and final positions of the minute hand apart?
A) 450
B) 600 C)
750 D) 900
Answer: B
Explanation :
The hour hand makes 1/2° in one minute.
To make 65°, the time taken is (650 / (1/2)) = 130
minutes.
So, the minute hand moves 130-minute spaces in this period.
130 minutes = 2 hours and 10 minutes.
In one hour, the minute hand makes one complete revolution, and in
one minute, the minute hand makes 6°.
After 2 hours, the minute hand will reach the initial position.
Therefore, the initial and final positions of the minute hand will
be (10 x 6°) = 60° apart.
36) The minute hand of a clock overtakes the hour
hand at intervals of 65 minutes of correct time. How much in a day does the
clock gain or lose?
a)
11 11/143 minutes b)10
10/143 minutes c)12
11/143 minutes
9
11/143 minutes
Answer :
Explanation :
In
a regular clock, the minute hand overtakes the hour hand at regular intervals
of 65 5/11 minutes
However,
in this clock, the two hands meet every 65 minutes, resulting in a gain of (65
5/11 – 65 ) = 5/11 minutes per interval.
In
one minute, the clock gains 5/11 minutes
In
65 minutes , it gains =>5/(11 x 65) minutes
The
gain in every 65 minutes is 5/11 minutes.
The
gain in 1 minute => 5/11 x 1/65
Therefore,
the clock gains in 24 hours (in a day)
=> 5/11 × 1/65 × 24 × 60 = 1440/143 minutes
or 10 10/143 minutes
37) In a
clock, the two hands coincide with each other at regular intervals of 72
minutes. What approximate time does the clock gain or lose in a day?
A) 131 minutes B) 46 minutes C)
164 minutes D) 87 minutes
Answer: A
Explanation :
The two
hands of a correct coincide with each other at regular intervals of 65 5/11
minutes.
The
two hands of the given clock coincide with each other at regular intervals
of 72 minutes.
In 72 minutes, the clock loses => 72- 65 5 /11 = 6 6/11 or 72/11 minutes
In 1 minute, the clock loses => 1/72 x 72/11 = 1/11 minutes
In a day or 24 hours, the clock loses => 1/11 x 24 x 60 =131 minutes
approximately
38) The wall clock, which gains uniformly, was observed to be 6
minutes slow at 7:30 a.m. on Sunday. On the same day at 9:30 p.m., the wall
clock was observed to be 1 minute fast. At what time did the wall clock show
the correct time?
a)7:30 p.m b)4:15 p.m c)6:30
p.m d)8 p.m
Answer: A
Explanation:
The time duration from 7:30 a.m. to 9:30 p.m.
is 14 hours.
The clock was 6 minutes slow at 7:30 a.m. and
was 1 minute fast at 9:30 p.m.
The total time gained by the clock in 14
hours is (6 + 1) = 7 minutes.
To gain 7 minutes, the clock takes 14 hours.
To show the correct time, the clock had to
gain 6 minutes from 7:30 a.m.
To gain 6 minutes, the
clock will take => 14/7 x 6 = 12 hours.
Therefore, the time at which the clock showed
the correct time is (7:30 a.m. + 12 hours) = 7:30 p.m.
39) A clock was 3 minutes slow at 4 a.m. on Sunday and 2 minutes
fast at 4 p.m. on Tuesday. When did it show the correct time?
A) 5 a.m. Monday B) 6:30 a.m. on Tuesday C) 5 p.m. on Monday D)
2:30 a.m. on Tuesday
Answer: A
Explanation:
The number of hours from 4 a.m. on Sunday to
4 p.m. on Tuesday is 60 hours.
The clock was 2 minutes slow at 4 a.m. on
Sunday and 2 minutes fast at 5 p.m. on Tuesday, so it gains (2 + 3) = 5 minutes
in 60 hours.
To gain 1 minute, the clock takes 60/5 = 12
hours.
If the clock gains 3 minutes from 5 a.m. on
Sunday, it will show the correct time.
To gain 3 minutes, it will take 3 x 12 hours
= 36 hours.
Therefore, the correct time was 24 hours after
4 a.m. on Sunday, which is 4:00 p.m. on Monday.
40) A
clock gains 2 minutes every hour and it is set to the correct time at 11:00
a.m. What is the true time when the clock shows the time 5:12 p.m. on the same
day?
A) 4.45 p.m B) 5:24 p.m C) 5 p.m D)
4:52 p.m
Answer: C
Explanation :
The time
interval from 11 a.m. to 5:12 p.m. =6 hours 12 minutes or 372 minutes
The clock gains 2 minutes in one hour.
62 minutes of the clock = 60 minutes of
the correct clock
1 minute of the clock = 60/62 or 30/31 minutes of the correct clock.
372 minutes of the clock = 30/31 x 372 = 360 minutes of the correct clock
360 minutes = 6 hours which is 12
minutes less than the time in the given clock.
Therefore, the correct time is => 5 : 12 p.m – 12 minutes = 5 p.m
41) The clock
tower in a town has a minute hand of length 4.2 meters. What is the area
covered by the minute hand in 20 minutes?
A) 21.25
cm² B) 17.5 cm² C) 18.48 cm² D) 23.7 cm²
Answer: C
Explanation:
If the
minute hand moves for 60 minutes, it completes a full circle.
In this
case, it moves for only 25 minutes, forming a sector.
Length of
the minute hand = Radius = 4.2 meters
The angle
made by the minute hand in 25 minutes = 20 x 6 = 120 (as in 1 minute, the
minute hand makes 6 degrees)
Area of the
sector with radius r and angle θ = π r² x θ/360
Area covered
by the minute hand in 25 minutes = π x 4.2² x 120/360
Therefore, the correct answer is 18.48 cm²12.
42) Two clocks, A and B, are in play. Clock A has its hands moving clockwise, while clock B, due to a reverse connection, has its hands moving counterclockwise. Initially, both clocks are set to 12. If, after a certain duration, the angle between the two-hour hands is 90º (for the first time), what will be the angle between the two-minute hands at the same instant?
Answer :A
Explanation :
Clock A has its hands
moving clockwise, while clock B, due to a reverse connection, has its hands moving
counterclockwise.
Initially, both clocks
show the time at 12.
After some time, the
angle between the hour hands of the two clocks is 90º (for the first time).
The angle between the
two-hour hands after some time is 90º, with the hour hand of clock A moving 45º
from its initial position and the hour hand of clock B also moving 45º in the
opposite direction.
The hands of both clocks
move 180º in either direction, resulting in the minute hands of the two clocks
coinciding, i.e., the angle between them becomes zero degrees.
A) 12.1 cm B)
48.4 cm C) 121 cm D) 84 cm
Answer: A
Explanation :
The tip of
the minute hand covers the total circumference of the dial in one minute.
The
length of the minute hand or radius r= 7.7 cm
In 60
minutes, the distance covered by the tip of the minute hand = 2 π r
In 15 minutes or ¼ th of th hour, the tip of the minute hand is => ¼ x 2 π r
=1/4 x 2 x 22/7 x 7.7 cm
= 12.1 cm approximately
44) The length of the minute hand of a clock is 6.3 cm, and the
hour hand is 4.1 cm. What distance does the tip of the minute hand cover in 20
minutes?
A) 13.2 cm B) 14.1
cm C)
12.6 cm D) 10.5 cm
Answer: A
Explanation:
The tip of the minute hand covers the total
circumference of the dial in one minute.
The length of the minute hand or radius r =
6.5 cm.
In 60 minutes, the distance covered by the
tip of the minute hand is 2πr.
In 20 minutes or 1/3rd of an hour, the
distance covered by the tip of the minute hand is 1/3 x 2πr.
= 1/3 x 2 x 22/7 x 6.3
= 13.2 cm
45) A
clock goes fast by 3 minutes during the first hour, by 7 minutes at the end of the
second hour, by 11 minutes at the end of 3rd hour, by 15 minutes at the end of the
fourth hour, and so on. At which hour, will the clock be fast by 39 minutes?
A) 12 B) 10 C) 8 D) 14
Answer: B
Explanation :
The clock gains 3 minutes in the first hour,
gains 7 minutes at the end of the second hour, gains 11 minutes at the third
hour, and so on.
Every hour, the clock goes fast by 4 minutes
more than the previous hour.
Therefore, all the terms are in an arithmetic
progression.
Let a=3 be the first term, d=4 be the common
difference, and the nth term be 39.
The nth-term formula for an arithmetic
progression is =a+(n−1)d.
So, 3 + (n−1) × 4 = 39
⇒4n-1 = 39
⇒ 4n=40
⇒ n=10.
At the end of the 10th hour, the clock will
be fast by 39 minutes.
Therefore, the correct answer is 10.
