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1.
At what time between 5 and 6 o'clock. The hands of a clock coincident
  • A.
    		 27 3  min. past 5  
    11
  • C.
    		 26 1  min. past 5  
    4
  • B.
    27 min. past 5
  • D.
    		 25 1  min. past 5  
    2
  • Answer & Explanation
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Answer : [A]
Explanation :
At 5 o’clock the hour hand is at 5 and the minute hand is at 12, (i.e) they are 25 min spaces apart.
To be together, the minute hand must gain 25 minutes over the hour hand.
25 minutes will be gained in =
60
55
x 25 =
12
11
x 25 =
300
11
= 27
3
11
 min.    
 
  The hands will coincide at 27
3
11
 min. past 5.    
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2.
At what time between 12 and 1 o'clock both the hands will be at right angles?
  • A.
    		 540  min. past 12  
    11
  • C.
    		 150  min. past 12  
    11
  • C.
    		 180  min. past 5  
    11
  • D.
    Both a) and b)
  • Answer & Explanation
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Answer & Explanation : [D]
Explanation :
At 12 o’clock the minute hand and hour hand coincide (i.e) they are 0° apart.
Now, when the two hands are at right angles, they are 15 min.
spaces apart. So they are at right angles in following 2 cases:
Case (i) When minute hand is 15 min. spaces behind the hour hand:
In this case, minute hand will have to gain 15 – 0 = 15 minutes spaces
55 minutes spaces are gained in = 60 min.
15 minutes spaces will be gained by it in =
60
55
x 15 =
180
11
 min.    
 
  They are at right angles at =
180
11
 min. past 12.    
Case (ii) When the minute hand is 15 min. spaces ahead of the hour hand:
The similar right angle occurs at =
180
11
x 3 =
540
11
 min. past 12.    
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3.
A clock is set right at 1 p.m. If it gains one minute an hour, what is the true time when the clock indicates 6 p.m. on the same day?
  • A.
    		 4 56  min. past 5 p.m  
    61
  • C.
    		 55 5  min. past 5 p.m  
    61
  • B.
    		 42 56  min. past 5 p.m  
    61
  • D.
    		 52 4  min. past 5 p.m  
    5
  • Answer & Explanation
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Answer : [C]
Explanation :
Total number of hours from 1 p.m to 6 p.m on the same day = 5 hours
The clock gains 1 min in 1 hour
 
  It gains 24 min. in 24 hours    
 
  24 hrs in 24 min. in 24 hours    
24 hrs 24 min. of this clock = 24 hrs of correct clock
 
 
122
5
 hrs. of this clock = 24 hrs of the correct clock    
 
  5 hrs of this clock = 24 x
5
122
 x 5 = 4
56
61
 hrs. of correct time        
 
  The correct time is 4
56
61
 hrs. after 1 p.m.    
= 5 p.m and
56
61
 x 60 min. = 5 p.m. and
3360
61
 min.
= 5 p.m and 55
5
61
 min. (i.e) 55
5
61
 min. past 5 p.m.
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4.
At what time between 7 and 8 o'clock will the angle between the two hands of a clock be 0°?
  • A.
    7.36
  • C.
    7.35
  • B.
    7.40
  • D.
    7.38
  • Answer & Explanation
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Answer : [D]
Explanation :
At 7 o'clock the hour hand is at 7 and the minute hand is at 12, (i.e) they are 35 min. spaces apart.
To be together, the minute hand must gain 35 min. over the hour hand.
55 min are gained in 60 min.
 
  25 min. will be gained in =
60
55
 x 35    
  =
12
11
 x 35 =
420
11
 = 38
2
11
 min.  
(i.e.) 38
2
11
 min. past 7. (i.e.) = 7.38    
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