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31.
A runs 1
3
8
 times As fast as B. If A gives B a start of 120 m and they reach the goal at the    
same time. The goal is at a distance of
  • A.
    360 m
  • C.
    460 m
  • B.
    440 m
  • D.
    380 m
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Answer : [B]
Explanation :
 
The speed of A and B are in the ratio 11 : 8.
 
Let speeds be 11s and 8s (in m/sec)
 
Let race be of x m
 
Then time taken by A to run xm is same as that of B to run (x 120) m.
 
 
 
x
11s
=
x - 120
8s
 
 
 
  3x = 11 x 120  
 
 
  x = 440.  
 
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32.
Two boys A and B run at 4
1
2
 and 6 km an hour, Respectively. A having 190 m start.    
The course being 1 km, B wins by a distance of
  • A.
    60 m
  • C.
    45 m
  • B.
    65 m
  • D.
    75 m
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Answer : [A]
Explanation :
 
Speeds (in m/sec) of A and B are
9
2
x
5
18
=
5
4
 and 6 x
5
18
=
5
3
, respectively  
 
A has a start of 190 m. So A has to run 1000 190 = 810 m while B 1000 m.
 
Time taken by B to cover 1000 m =
3
5
 x 1000 = 600 sec.    
 
In this time A covers
5
4
 x 600 = 750 m.    
 
So B reaches the wining post while A remains 810 750 = 60 m behind.
 
 
  B wins by 60 m.  
 
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33.
In a race of 600 m. A can beat B by 60 m and in a race of 500 m. B can beat C by 50 m. By how many m will A beat C in a race of 400 m?
  • A.
    364 m
  • C.
    324 m
  • B.
    254 m
  • D.
    354 m
  • Answer & Explanation
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Answer : [C]
Explanation :
 
Clearly, if A runs 600 metres, B runs = 540 m
 
 
  If A runs 400 m, B runs =  
540
600
 x 400    = 360 metres  
 
Again, when B runs 500 m. C runs = 450 m
 
 
  When B runs 360 m. C runs =  
450
500
 x 360    m = 324 m.  
 
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34.
X, Y and Z are the three contestants in one km race. If X can give Y a start of 50 metres and X can also give Z a start of 69 metres, how many metres start Y can give Z?
  • A.
    10 m
  • C.
    20 m
  • B.
    40 m
  • D.
    25 m
  • Answer & Explanation
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Answer : [C]
Explanation :
 
Here X becomes Ist, Y becomes IInd and Z becomes IIIrd in the race.
 
 
  (L - x12)x23 = L(x13 - x12)    
 
Where,
 
Ist (X) gives IInd (Y) a start of x12 = 50 metres
 
Ist (X) gives IIIrd (Y) a start of x13 = 69 metres
 
IInd (Y) gives IIIrd (Z) a start of x23 = ?
 
    Length of race(L)  = 1000 metres    
 
 
  (1000 - 50)x23  = 1000(69 - 50)    
 
 
  x23  = 20 metres.    
 
Hence Y gives Z a start of 20 metres.
 
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35.
In a 100 metres race, A can beat B by 25 metres and B can beat C by 4 metres. In the same race, A can beat C by -
  • A.
    29 metres
  • C.
    28 metres
  • B.
    21 metres
  • D.
    26 metres
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Answer : [C]
Explanation :
 
A : B = 100 : 75 and B : C = 100 : 96
 
 
  A : C =
A
B
x
B
C
=
100
75
x
100
96
=
100
72
 = 100 : 72  
 
So, A beats C by (100 72) = 28 metres
 
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