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)

= 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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