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16.
A and B run a 5 km race on a round course of 400 m. If their speeds be in the ratio 5 : 4, how often does the winner pass the other?
  • A.
    4
    1  times  
    2  
  • C.
    2
    3  times  
    4  
  • B.
    3
    1  times  
    2  
  • D.
    2
    1  times  
    2  
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Answer : [D]
Explanation :
 
When A makes 5 rounds, B makes 4 rounds.
 
In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time. When A makes 5 rounds.
 
Distance covered by A in 5 rounds =
5 x 400
100
 = 2 km  
 
  In covering 2 km. A passes B 1 time    
 
 
  In covering 5 km. A passes B =
5
2
 = 2
1
2
 times.    
 
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17.
In a 100 m race, A runs at 5km/hr. A gives B a start of 8 m and still beats him by 8 sec. Find the speed of B
  • A.
    6.14 km/hr
  • C.
    3.14 km/hr
  • B.
    4.14 km/hr
  • D.
    2.14 km/hr
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Answer : [B]
Explanation :
 
Time taken by A to cover 100 m = 100 +   5 x
5
18
   = 72 sec.  
 
 
  B covers (100 8) or, 92 m in (72 + 8) or, 80 sec.  
 
 
  Speed of B =
92
80
x
16
5
 = 4.14 km/hr.  
 
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18.
A can run 20 metres while B runs 25 metres. In a km race B beats A by -
  • A.
    250 metres
  • C.
    200 metres
  • B.
    225 metres
  • D.
    125 metres
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Answer : [C]
Explanation :
 
In a 25 metres race B beats A by 5 metres.
 
In one km race B Beats A by  
5
25
 x 1000    = 200 metres        
 
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19.
A runs 1
1
3
 as Fast as B. If A gives B a start of 30 minutes. How far must be the wining post,      
so that the race ends in a dead heat?
  • A.
    150 m
  • C.
    120 m
  • B.
    100 m
  • D.
    None of these
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Answer : [C]
Explanation :
 
Assuming L = distance of the winning post such that the race ends in a dead heat, i.e., booth the participants A and B reach the wining post at the same time.
 
 
  Time taken by A = time taken by B  
 
 
 
L
4
3
v
=
L - 30
v
       
 
 
  L = 120  
 
  Since t =
d
v
,  Where d = distance and v = speed    
 
 
  Length of race (distance) of wining post is 120 metres.  
 
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20.
A can run a kilometre in 4 min. 54 sec. and B in 5 min. How many metres start can A give B in a km race so that the race may end in a dead heat?
  • A.
    20 metres
  • C.
    18 metres
  • B.
    16 metres
  • D.
    14.5 metres
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Answer : [A]
Explanation :
 
Distance covered by B in 6 seconds =  
1000
300
 x 6    metres = 20 metres        
 
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