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Problems on Clocks  For complete understanding of the concept of clocks, go through  Concept of Clocks Aptitude   Clocks - Solved Pro...

Quantitative Aptitude Questions - Problems on CLOCKS Solved

Problems on Clocks 
For complete understanding of the concept of clocks, go through Concept of Clocks
Aptitude   Clocks - Solved Problem 1
What is the angle made by the minute angle in 16 minutes?
 a)  80                       b)320                 c)960                   d) 480            e)900
Answer: C
Explanation:
The angle made by the minute hand in 1 minute is 60.
In 16 minutes, the angle made by the minute hand   = 16 x  6=960
Aptitude   Clocks - Solved Problem 2
2. What is the angle made by the hour hand in 30 minutes?
a)  50                 b)100                c)1800             d) 150                 e)280
Answer : D
Explanation:  
 The angle made by the hour hand in 1 minute is  $\frac{1}{2}$ 0 .
   In 16 minutes, the angle made by 30 minutes is = 30 x  (½)
                                                                         =150
Aptitude  Problem on  Clocks - Solved Problem 3
3. What is the difference between angles made by minute hand and hour hand in 24 minutes?
a)  1850                       b)1200                c)1800           d) 1320                              e)2080
Answer: D
Explanation : The angle made by the minute hand in 24 minutes = 24 x  60 =1440
                    The angle made by the hour hand in 24 minutes    =24  x (½)=120
                                         The difference is = 1440 -120 =1320

Aptitude Problems on  Clocks - Solved Problem 4
4. How often the hands of clock at right angle everyday ?
a)11 times               b)22 times               c)44 times     d)55 times     e)66 times
Answer : C
Explanation:
In onehour there are two positions in which the minute hand and hour hand are at right angle.
          Each of these positions is repeated 22 times in every 12 hours.
    Therefore in a day ( 24 hours ), the two hands are perpendicular to each other
ð     22 + 22 =44 times.
Aptitude   Clocks - Solved Problem 5
5. How many times the hands of a clock are in a straight line every day?
     a) 11 times         b)22 times           c)33 times            d)44 times     c)55 times
 Answer : D
Explanation: Any relative position of the two hands of a clock is repeated 11 times in every 12 hours.
 In every 12 hours, two hands coincide ( when the two hands coincide, they are always in the same straight line ) 11 times   and two hands are opposite to each other (but in the same straight line )11 times .
   In 12 hours , two hands are in straight line  11 +11 =22 times.
     In every 24 hours , two hands are in straight line  44 times.
Aptitude Questions on Clocks - Solved Problem 6
6.  A clock strikes 5 takes 16 seconds. In order to strike 10 at the same rate, the time taken is  
a) 24 seconds   b)30 seconds         c)36 seconds         d)32 seconds  e)40 seconds         
Answer : C
Explanation :
There are 4 intervals when the clock strikes 5.
Time taken for  4 intervals = 16 seconds
  Time taken for  1 interval = 4 seconds
  In order to strike 10, there are 9 intervals, for which the time taken is 9 x 4 =36 seconds
Aptitude questions on  Clocks - Solved Problem 7
7. What is the angle between the minute hand and the hour hand at 20 minutes past 4 O' clock ?
     a)  50    b)100             c)1800        d) 150             e)200
Answer : B   
Explanation :  To find the angle between hour hand and minutes at   H hours M minutes , 
                                      θ = |(30 X H) -  $\frac{11}{2}$ M |
                                        =  |(30 X 4) -($\frac{11}{2}$ )x 20 |
                                        =  |120 -  110 | = 100
Aptitude questions on  Clocks - Solved Problem 8
8.At what time between 4 and 5’O clock are the two hands of the clock coincide ?
a)4.21 $\frac{9}{11}$              b)4.20           c)4.23 $\frac{7}{11}$              d)4.22           e)4.19 $\frac{9}{11}$
Answer : A
Explanation : At 4'O clock , the hour hand is at 4 and the minute hand is at 12. Hence minute hand is 20 minutes spaces behind the hour hand.
 The two hands will coincide each other, when the minute hand gains 20 minutes spaces over the hour hand.
The minute hand gains 55 minute spaces in 60 minutes .
To gain 1 minute space , it will take $\frac{60}{55}$ minutes.
To gain 20 minute spaces, it will take 20 x $\frac{60}{55}$ = 20 x $\frac{12}{11}$ =21 $\frac{9}{11}$ minutes 
              The two hands coincide at 21 $\frac{9}{11}$ minutes past 4.
Aptitude Problems on  Clocks - Solved Problem 9
9.  Find the time between 8 and 9’O Clock when the two hands of a clock are in the same straight line.
a) 8.41 $\frac{9}{11}$             b)8.43 $\frac{7}{11}$     c)8.47 $\frac{3}{11}$     d)8.44 $\frac{3}{11}$     e)None the above
Answer: B
Explanation :
Two hands of a clock are in the same straight line in two cases:
Case 1: 
When the two hands are in exactly opposite direction.
This equals 180o=$\frac{180^{0}}{6}$ =30 minute spaces apart.
At 8’O Clock, the minute hand is (8×5)=40 minute spaces behind the hour hand. Therefore, the minute hand will have to gain (40-30)=10 minute spaces over the hour hand.
55 minutes spaces are gained in 60 minutes
 To Gain of 40 minute spaces => 10 x $\frac{60}{55}$ =$\frac{120}{11}$ = 10 $\frac{10}{11}$ minutes.
 The minute hand will be is exactly opposite direction to the hour hand at 10 $\frac{10}{11}$ minutes past 8’O Clock.
Case 2: 
When the two hands coincide i.e, 0 minute spaces apart.
        In this case, the minute hand will have to gain (8×5)=40 minute spaces over the hour hand.
        To gain 40 minute spaces=>$\frac{60}{55}$ ×40=$\frac{480}{11}$ = 43 $\frac{7}{11}$ times
    The two hands will hands will coincide at 43 $\frac{7}{11}$ minutes past 8 ‘O Clock.
Aptitude questions on Clocks - Solved Problem 10
10.  At what time between 5 and 6’O clock will the two hands of a clock be at right angle?
a) 5.43 $\frac{7}{11}$    b)5.10 $\frac{10}{11}$             c)5.12 $\frac{8}{11}$     d)5.13 $\frac{8}{11}$     e) 5.09 $\frac{7}{11}$
Answer : Both A and B
Explanation: At 5’O Clock the minute hand is (5×5)=25 minute spaces behind the hour hand.
The two hands will be at a right angle when either (i) the minute hand is 15 minute-spaces behind the hour hand or (ii) the minute hands are 15 minute-spaces ahead of the hour hand.
Case1: When the minute hand 15 minute-spaces behind the hour hand.
For the two hands to be in this position, the minute hand must gain (25-15) =10 minute-spaces over the hour hand.
 55 minute spaces are gained in 60 minutes.
 So10 minute-spaces are gained in =>  $\frac{60}{55}$ ×10=$\frac{120}{11}$ =10 $\frac{10}{11}$ minutes.
 Therefore , the two hands will be at right angle at 10 $\frac{10}{11}$ minute past 5’O clock.
Case 2: when the minute hand 15 minute-spaces ahead of the hour hand.
                To be in this position, the minute hand must gain (25+15)=40 minute spaces.
                So 40 minute-spaces are gained in=>  $\frac{60}{55}$ ×40 =$\frac{480}{11}$ =43 $\frac{7}{11}$ times.
 Therefore , the two hands will be at right angle at 43 $\frac{7}{11}$ minutes past 5’O Clock.
Aptitude questions on  Clocks - Solved Problem 11
11.  At what time between 4 and 5 are the hands 2 minutes spaces apart?
a) 4 19 $\frac{7}{11}$ and 4.22
b)4.21 $\frac{7}{11}$ and 4.24
c) 4. 19 $\frac{7}{11}$ and  4.24
d) 4.18 $\frac{9}{11}$   and 4.24 $\frac{2}{11}$
e) None of the above
Answer : C
Explanation: 4’O Clock, the two hands are 20 minute spaces apart.
Case 1:  When the minute hand is 2 minute spaces behind the hour hand.
 In this case, the minute hand will have to gain (20-2) i.e 18 minute spaces. Now, we know that 18 minute spaces will be gained in 18 × $\frac{12}{11}$ = $\frac{216}{11}$ =19 $\frac{7}{11}$ minute.
Therefore , the two hands will be 2 minutes apart at 19 $\frac{7}{11}$ minutes past 4.
Case 2: when the minute hand is 2 minute spaces ahead of the hour hand.
                In this case, the minute hand will have to gain (20+2) i.e., 22 minute spaces.
                Now the 22 minute spaces will be gained in
                22× $\frac{12}{11}$ = 24 minutes
 The hands will be 2 minute spaces apart at 24 minute past 4

 Aptitude Questions on Clocks - Solved Problem 12
When do the two hands of a clock of just after 3 pm make 30 º angles between them? 
a)3:15:00    b)3:10:54    c)3:01:59    d) 3:20:21      e)3:18:00
Answer:(B)
Explanation: To find the angle between hour hand and minutes at   H hours M minutes, 
                                      θ =|30H – $\frac{11}{2}$ M|
Here the angle given is 30=> - 30 = 30 x 3 – $\frac{11}{2}$ M ( We take + and – angles , because minute hand is 300 behind the hour hand once  and  300 ahead of  the hour hand another time)
$\frac{11}{2}$ M = 60  => M= $\frac{120}{11}$ = 10 $\frac{10}{11}$ minute
              = 10 min 54s
(We have the answer in the given choices, we need not compute the another time with +300)
    Required time = 3:10:54

Aptitude problems on Clocks - Solved Problem 13
A clock strikes ones at 1 O’clock, twice at 2 O’clock and so on. What is the total number of striking in a day
a) 12                 b) 156           c) 78            d) 24            e) 48
Answer:(B)
Explanation: The clock strikes once at 1 O’clock, twice at 2 O’clock, thrice at 3 O’clock and so on.
So in 12 hours, the total number of striking = 1 + 2 + 3 + 4 + ---- + 12
                                                         (Sum of the first n natural numbers= $\frac{n(n+1)}{2}$ )
                                            = 12 x $\frac{(12+1)}{2}$ (12+1)/2 =78
     In 12 hours, the total striking are 78.
          In a day (24 hours) , total number of striking = 2 x 78 = 156

Aptitude questions on  Clocks - Solved Problem 14
Three cuckoo clocks are such that the cuckoos chime after every 9 minutes, 15 minutes and 35 minutes respectively. If the 3 clocks chime simultaneously at 3 p.m, what time will they chime together again?
a)8 :15 p.m             b)9:15 p.m    c)10.30 p.m       d) 11.00 p.m            e)00.45 p .m
Answer:B
Explanation:
Three cuckoo clocks are such that the cuckoos chime after every 9 minutes, 15 minutes and 35 minutes respectively.
All the three clock chime simultaneously at 3 p.m
They will again chime together => LCM of 9 minutes, 15 minutes and 35 minutes
ð  315 minutes or 5 hours 15 minutes
After 5 hours 15 minutes , all the three clock will chime together
 The time at they will chime again together = 3 p.m + 5 hours 15 minutes
                                                               = 8:15 p.m

Aptitude problems on Clocks - Solved Problem 15
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 $\frac{11}{143}$ minutes                 b)10 $\frac{10}{143}$ minutes           c)12 $\frac{11}{143}$   minutes
d)   9 $\frac{11}{143}$   minutes                  e) 13 $\frac{11}{143}$ minutes
Answer: B
Explanation:
In a correct clock, the minute hand gains 55 minute spaces over the hour hand in 60 minutes.
To coincide each other again, the minute hand must gain 60 minutes over the hour hand.
Now, 55 min. are gained in 60 min.
          60 min. are gained in $\frac{60}{55}$ x 60 min. = 65 $\frac{5}{11}$ min.
But in the given question, the minute hand overtakes the hour hand at regular intervals of 65 minutes ..
In the given clock, the two hands meet at 65 minutes instead of 65 $\frac{5}{11}$ min.
                Gain in every 65 minutes. =65 $\frac{5}{11}$ -65  min. = $\frac{5}{11}$ min.
In 65 minutes , the clock gains $\frac{5}{11}$ minutes.
The clock gains in a day (24 hours) = $\frac{5}{11}$  X $\frac{1}{65}$ X 24 X 60 = $\frac{1440}{143}$ minutes = 10 $\frac{11}{143}$

Aptitude difficult problems Clocks - Solved Problem 16.
There are two clocks A and B. The hands of the clock A moves normally as clockwise while in clock B (due to reverse connection) they move anticlockwise. Initially the two hands of both clocks are at 12. If after some time, the angle between the directions of two hour hands is 90º for the first time , then at the same instant the angle between the directions of minute hand will be
a)00                      b) 60º                    c) 120º                    d)180º         e) 900
Answer: A
Explanation: The angle between the two hour hands after some time is 900.
As the both started at 12 ‘o clock, the hour hand of clock A makes 450 and the hour hand of clock B makes 450 from their initial position.
The hour hand of clock A moved 45º from its initial position. Therefore, number of minutes the hour hand makes is 45 x 2 = 90 minutes
In 90 minutes, the minute hand makes angle of   90 x 6 0 = 5400
As 3600 is a complete revolution = > 5400 = (3600 + 180º) from its initial position.
As both hands move 1800 in either direction, the minute hands of two clocks coincide, i.e. the angle between them is zero degree.

Aptitude questions on Clocks - Solved Problem 17
A watch was set correct at 12’O clock.  It loses 10 minutes per hour. What will be the angle between the two hands of the clock after 1 hour?
a)    75º           b) 85º            c) 90º               d) 105º              e)1200
Answer:(B)
Explanation:
            The clock loses 10 minutes per hour
           S the clock shows only 50 minutes for every 60 minutes.
After 1 hour, the watch show the time 12:50
The angle between the two hands of the clock after 1 hour i.e 60 minutes
    (i.e. 50 minutes according to the clock)  = |30H – $\frac{11}{2}$ M|
                                                            =|30 x 12 – $\frac{11}{2}$ x 50|
                                                               = |360º – 275º| = 85º

Aptitude problems on Clocks - Solved Problem 18
A clock is set right at 7:10 am on Thursday, which gains 12 minutes in a day. Find the true time when this clocks the shows the 3:50 p.m on the following Sunday?
a)2:50 pm          b) 3:10 pm       c) 3:30 pm            d)4:30 pm      e) 4.10 p.m
Answer: B
Explanation: Total number of hours from Thursday 7.10 a.m. to the 3 : 50 p.m . on Sunday.
=>24 x 3 + 8 hours 40 minutes = 80 hours 40 minutes. (80 $\frac{40}{60}$ = $\frac{242}{3}$ hours)
The clock gains 12 minutes in every 24 hours.
     24 hours 12 min. of this clock =24 hours of correct clock,
 i.e.   $\frac{121}{5}$ hours of this clock = 24 hours of correct clock
∴   80 hours 40 minutes of this clock =24 X $\frac{5}{121}$ X  $\frac{242}{3}$  hours of correct clock
                                                 = 80 hours of correct clock
     Therefore the correct time is 7:10 a.m + 80 hours = 3:10 p.m.

Aptitude difficult questions on Clocks - Solved Problem 19
A clock is set right at 10 a.m on Tuesday . The clock gains 10 min in 24 hours. What will be the correct time when the clock shows the time 8 p.m on the following Thursday?
a) 8.36 p.m.       b) 8.40 p.m.            c)7.36 p.m.              d) 7.52 p.m             e)8.12 p.m
Answer: A
Explanation:
Total number of hours from Tuesday at 10 a.m. to the following Thursday at 8 p.m.
ð  24 x 2 + 10 = 58 hours
     24 hours 10 minutes of this clock = 24 hours of a correct clock.
     $\frac{145}{6} Hours of the incorrect clock = 24 hours of correct clock.
     58 hours of the incorrect clock = 24 X $\frac{6}{145}$ X 58 hours of correct clock
                                                  =  57 $\frac{3}{5}$ $\frac{3}{5}$ hours of correct clock.
                                                  = 57 hours 36 minutes
          
     Thus, the correct time on the following Wednesday will be 8.36 p.m.

Aptitude Clocks - Solved Problem 20
A clock was correct at 2 p.m, but then it began to lose 30 minutes each hour. It now shows 6 pm, but it stopped 3 hours ago. What is the correct time now?
a)8.30 pm.        B)12 midnight           c)11 p.m.               d)1.30 a.m.              e)1 a.m
Answer: E
 Explanation : The clock loses 30 minutes per hour. And the clock set correct at 12 noon.
              30 minutes of this clock = 60 minutes of the correct clock
         From 2 p.m to 6 p.m , total number of hours = 4 hours
                 4 hours of this clock => 4 x $\frac{60}{30}$ = 8 hours
             The correct time when the clock show 6 p.m = 6 p.m + 4 = 10 p.m

          The clock stopped 3 hours ago , So present time is 10 p.m + 3 hours = 1 a.m