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21.
In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?
  • A.
    100
  • C.
    300
  • B.
    200
  • D.
    400
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Answer : [A]
Explanation :
 
Suppose, x points make the game.
 
Clearly, when A scores x points, B scores (x - 20) points and C scores (x - 32) points.
 
Now, when B scores x points, C scores (x - 15) points
 
When B scores (x - 20) points.
 
C scores  
(x - 15)
x
 x (x - 20)    points  
 
 
 
(x - 15)(x - 20)
x
 = x - 20 or, x = 100    
 
Hence, 100 points make the game.
 
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22.
In a game A can give B 25 points in 75 and C 18 points in 90. How many points can C give B in a game of 120?
  • A.
    20
  • C.
    40
  • B.
    30
  • D.
    50
  • Answer & Explanation
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Answer : [A]
Explanation :
 
When A scores 75 points, B scores 50 points
 
When A scores 90 points. C scores (90 - 18) = 72 points
 
 
  When A scores 75 points, C scores =
72
90
 x 75 = 60 points        
 
  A : B : C = 75 : 50 : 60      
 
  C : B =
60
50
=
120
100
 
 
 
  So, in a game of 120, C can give B (120 - 100) = 20 points  
 
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23.
A and B run a km race. If A gives B a start of 50 m, A wins by 14 sec and if A gives B a start of 22 sec km, B wins by 20 m. The time taken by A to run a km is:
  • A.
    100 sec
  • C.
    105 sec
  • B.
    120 sec
  • D.
    125 sec
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Let times (in sec) taken by A and B to run a km, be x and y, respectively.
 
When B gets a start of 50 m, B runs
 
1000 – 50 = 950 m while A runs 1000 m.
 
 
 
950
100
 y - x = 14,  
 
i.e. 0.95y - x = 14
 
and, When B gets a start of 22 sec, A runs (y - 22) sec, while B runs for y sec.
 
 
  1000 -
1000
x
 (y - 22) = 20  
 
i.e. 50y - 49x = 1100.
 
Multiplying (i) by 49 and subtract from (iii)
 
  3.45y = 414      
 
 
    y = 120 sec.    
 
 
  (i)
 
x = 0.95 x 120 - 14 = 100 sec.      
 
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24.
In a flat race, A beats B by 15 metres and C by 29 metres. When B and C run over the course together, B wins by 15 metres. Find the length of the course -
  • A.
    220 m
  • C.
    225 m
  • B.
    325 m
  • D.
    250 m
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Answer : [C]
Explanation :
 
Using (L - x12)x23 = L(x13 - x12)  
 
Where x12 = A beats B by 15 metres  
 
  x23 = B beats C by 15 metres  
 
  x13 = A beats C by 29 metres  
 
  L  = Lenght of course = ?  
 
 
(L - 15)15  = L(29 - 15)  
 
 
L  = 225 metres  
 
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25.
In a km race A can beat B by 80 m and B can beat C by 60 m. In the same race A can beat C by
  • A.
    135.2 m
  • C.
    142 m
  • B.
    130.5 m
  • D.
    132.5 m
  • Answer & Explanation
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Answer : [A]
Explanation :
 
While A runs 1000 m, B runs 1000 – 80 = 920 m and while B runs 1000 m, C runs 1000 – 60 = 940 m
 
 
  While B runs 920 m; C runs =
940
1000
 x 920 =
4324
5
 m  
 
 
  While A runs 1000 m, C runs
4324
5
 m  
 
 
  A can beat C by 1000 -
4324
5
=
676
5
 = 135
1
5
 m
 
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