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Wipro Latest Placement Papers Pattern - Model Questions Solved - Problems On clocks

                      Wipro Placement Papers - Model Problems on  Clocks 

Wipro Placement Papers with Solutions –Problems on  Clocks 1
In a conventional clock, how many times does the minute hand pass the hour hand between noon and midnight?
a) 10 times              b)11 times               c)12 times               d)15 times
Answer : A
Explanation :
In 12 hours, the hour hand goes around the dial just once and the minute hand goes around 12 times.
Therefore they pass each other (12 – 1) = 11 times.
              One of these 11 times is 12 midnight also. 
                         But between noon and midnight is asked.
                                 So we don’t count either noon or midnight  
Therefore the answer is 10.

Wipro Placement Questions with Answers – Problems on Clocks 2
How many times in a day, the hands of a clock are straight?
a) 22                               b) 24                      c) 44                      d) 48

 Answer : C
Explanation: Any relative position of the two hands of a clock is repeated 11 times every 12 hours.
 In every 12 hours, two hands coincide (when the two hands coincide, they are always on the same straight line ) 11 times  and two hands are opposite to each other (but in the same straight line )11 times.
              In every 12 hours, two hands are in a straight line 11 +11 =22 times.
                            ∴ In every 24 hours, two hands are in a straight line 44 times.

Wipro Placement Papers with Answers –  Clocks Solved Problem 3
How many times do the hands of a clock point towards each other in a day?
a)12                       b) 18                      c) 22                      d) 24
Answer : C
Explanation :
In one hour, the two hands point towards each other only once.
The hands of a clock point towards each other 11 times in 12 hours. (Because between 5 O.’ clock and  7 O’ clock, at 6 O’clock only they point towards each other)
         In 12 hours, it happens 11 times. Hence in a day ( 24 hours), 22 times.
          So, in a day the two hands point towards each other 22 times

Wipro Placement Questions with Solutions – Model Problems on Clocks 4
At 3.40, the hour hand and the minute hand of a clock form an angle of
a) 120°                   b) 125°                   c) 130°                   d) 135°

Answer: C
Explanation :
The direct formula to find the angle between two hands when the time in the clock is
H: M
                              Angle = |30H -$\frac{11}{2}$ M|
       Here the given time is 3: 40              H= 3 and M=40
 
                        Angle = |30 x 3 - $\frac{11}{2}$ x 40|
                                   =|90-220|   =  1300

Wipro Placement Papers with Answers – Clocks Solved Question 5
At what angle the hands of a clock are inclined at 15 minutes past 5?
a) $\frac{117}{2}$ °               b) 64 °                             c) $\frac{135}{2}$ °               d) $\frac{145}{2}$ °

Answer: C
Explanation :
The direct formula to find the angle between two hands when the time in the clock is
H: M
                              Angle = |30H -$\frac{11}{2}$ M|
       Here the given time is 5: 15              H= 5 and M=15
                        Angle = |30 x 5  - $\frac{11}{2}$   x 15|
                                   =|150 -87 ½|   =  $\frac{135}{2}$ 0

Wipro Placement Questions with Explanations – Model Question 6
Find the angle between the hour and the minute hand of a clock when the time is 3.25.
a) 47 ½                  b) 49 ½                  c) 55 ½                  d) 57 ½
Answer: A
Explanation :
The direct formula to find the angle between two hands when the time in the clock is H: M
                              Angle = |30H - $\frac{11}{2}$ M|
       Here the given time is 3: 25.              H=3 and M=25
                        Angle =|( 30 x 3_  - ($\frac{11}{2}$ x 25)|
                                   =|90 -  137.5|
                                   =  47.50  or 47 $\frac{1}{2}$0

Wipro Latest Placement Papers – Model Problems on Clocks 7
At what time between 2 and 3 o'clock, will the hands of a clock be together?
a) 10 $\frac{10}{11}$              b) 10 11/10                      c) 11 $\frac{10}{11}$              d) 12 $\frac{10}{11}$

Answer : A
Explanation:
Method 1:
At 2'O clock, the hour hand is at 2 and the minute hand is at 12. Hence minute hand is 10 minutes spaces behind the hour hand.
The two hands will coincide each other, when the minute hand gains 10 minutes spaces over the hour hand.
We know that, 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 minutes spaces, it will take    10 x $\frac{60}{55}$ = 10 x $\frac{12}{11}$ =10 $\frac{10}{11}$ minutes 
           The two hands coincide at 10 $\frac{10}{11}$ minutes past 2.
Method 2 :
When the two hands coincide, the angle between the two hands is 00.
The angle between the two hands, when the time in the clock is H:M is                                                                           Angle = 30 H - $\frac{11}{2}$ M
  Here we take the first hour as H, and we have to find the value of M.
    Angle = 30 H  - $\frac{11}{2}$ M
                                           00= 30 x 2   - $\frac{11}{2}$   x M
                                              =>$\frac{11}{2}$   x M = 60
                          =>  M = 60 x $\frac{2}{11}$ = 10 $\frac{10}{11}$ minutes
Therefore between 4 and 5 ‘O clock, the two hands coincide at 2 : 10 $\frac{10}{11}$ minutes

Wipro Placement Papers with Answers – Model Questions  8
At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
a) 5 $\frac{1}{11}$ °              b) 12 $\frac{4}{11}$°            c) 13 $\frac{4}{11}$°              d) 16 $\frac{4}{11}$°
Answer : C
Explanation :When the two hands coincide, the angle between the two hands is 00.
The angle between the two hands, when the time in the clock is H: M is                               
                  Angle = |30 H  -  $\frac{11}{2}$M|
  Here we take the initial hour as H, and we have to find the value of M.
                                             Angle = |30 H  -  $\frac{11}{2}$ M|
                                           00= |30 x 3   - $\frac{11}{2}$ x M|
ð   $\frac{11}{2}$ x M = 90
ð   M = 90 x $\frac{11}{2}$= 16 $\frac{4}{11}$ minutes
Therefore between 4 and 5 ‘O clock, the two hands coincide at 3:16 $\frac{4}{11}$ minutes

Wipro Latest  Placement Questions  - Model Problems on Clocks 9
Imagine a railway station clock with the second-hand on the same axis as the two other hands. How often in a 24-hour day, will the second-hand be parallel to either of the two other hands?
a) 5474                   b) 5174                            c) 5714                   d) 5724
Answer : C
Explanation :
In a 24-hour day, the second-hand will be 5714 times parallel to the two other hands.

Within any minute, the second-hand will twice be parallel to each of the two other hands, minute-hand and hour-hand.
Thus, there are (4*60*24) 5760 such parallel positions in one day.

But, the hour-hand and the minute-hand are parallel to each other 23 times in 12 hours i.e. 46 times in 24 hours. Therefore, 46 parallel positions have to be deducted.
Hence, the correct answer is  (5760 - 46)  = 5714
In  24-hours or a day, the seconds hand is parallel to either of the two hands 5714 times.

Wipro Placement Papers with Answers – Model Problems on Clocks 10
At how many points between 10 O'clock and 11 O'clock are the minute hand and the hour hand of a clock at an angle of 30 degrees to each other?
a)1                                  b)2                        c)3                         d)4
Answer :A
Explanation :
Between 10 and 11, the minute hand and hour hand are at an angle of 30o to each at
Case 1 :  When the minute hand is behind the hour hand
          300 = 30 x 10 – $\frac{11}{2}$ x m
ð  M = $\frac{540}{11}$
ð  49 $\frac{11}{11}$ minutes past 10.
Case 2 : When the minute hand is ahead of the hour hand
              -300 = 30 x 10 – $\frac{11}{2}$ M
ð  M = $\frac{600}{11}$ = 60 minutes after 11
First time they are 300 apart at 49 $\frac{1}{11}$ minutes past 10.
The next time they will be at the angle of 30o to each other will be at 11.
So only 1 time, it happens

Latest Wipro Placement Questions– Model Problems on Clocks 11
A Clock strikes every hour-once at 1.00, twice at 2.00, and so on. The clock takes 6 seconds to strike 5.00 and 12 seconds to strike 9.00. The time needed to strike 1.00 is negligible. How long does the clock need for all its striking in 24 hours?
a)168 Seconds                   b)178 Seconds         c)188 Seconds         d) 198 Seconds
Answer :D
Explanation :
The clock takes 6 seconds s to strike 5.00.
So there are 4 interval gaps between 5 strikes.
So the gap between each striking is $\frac{6}{4}$ = 1.5 seconds.
To strike 2.00, it takes = 1.5 seconds.
To strike 3.00 ,it takes = 3 seconds.
To strike 4.00 ,it takes = 4.5 seconds
................
................
To strike 12.00, it takes = 16.5 seconds.
So it takes a total of 1.5 + 3 + 4.5 + . . . . . . + 16.5
= 1.5 ( 1 + 2 + 3 + .... + 11) = 99 seconds to strike 12 hours.
For 24 hours the clock takes 99 × 2 = 198 seconds

Wipro Latest Placement Questions– Model Problems On Clocks 12
A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
a) 2 p.m. on Tuesday                   b) 2 p.m. on Wednesday    
c) 3 p.m. on Thursday                  d) 1 p.m. on Friday            
Answer :B
Explanation :
 Number of hours between noon (12 P.M) on Monday to 2 p.m on the following Monday  = 1 Week + 2 hours = 170 hours
The clock gains 2 minutes + 4 minutes 48 seconds (4 $\frac{48}{60}$ minutes) in 170 hours
    Thus the clock gains  (2 + 4 $\frac{4}{5}$ min ) in 170 hours
    i.e., the clock gains $\frac{34}{5}$ minutes in 170 hours
    Now $\frac{34}{5}$ minutes are gained in 170 hours
  To be correct, it has to gain 2 minutes from 12 p.m Saturday
    2 min are gained 170 x $\frac{5}{34}$   x 2  = 50 hours = 2 days 2 hours
      12 p.m Monday + 2 days 2 hours = 2 p.m. on Wednesday
        The clock was correct at 2 p.m on Wednesday.

Wipro Latest Placement Papers with Solutions – Model Problems on Clocks 13
A clock is set at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?
a) 9 p.m                  b) 10 p.m                c) 11 p.m                d) 12 p.m

Answer: C
Explanation: 
   Total number of hours from Today 5 a.m. to the 10 p.m. on the 4th day
ð  (24 hours x 3 days) + 17 = 59 hours
The clock loses 16 minutes in every 24 hours.
     23 hours 44 min. of this clock= 24 hours of the correct clock,
i.e. $\frac{356}{15}$ hours of this clock = 24 hours of correct clock
     89 hours of this clock =( 24 x $\frac{15}{356}$ x 89) hours of correct clock
                                       = 90 hours of the correct clock.
                  So the correct time is 1 hour more than 10 pm. i.e., 11 pm.