6.
In a game of 100 points A can give B 20 points and C 28 points. Number of points B can give C in a game of 100 points is
• A.
10
• C.
15
• B.
90
• D.
85
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Explanation :

A scores 100 while B scores 100 – 20 = 80 and C scores 100 – 28 = 72.

While B scores 80, C scores 72

While B scores100, C scores
 72 80
x 100 = 90

B can give C 100 - 90 = 10 points.

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7.
In a 200 metres rate A beats B by 35 m or 7 seconds. A’s time over the course is :
• A.
40 sec
• C.
33 sec
• B.
47 sec
• D.
None of these
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Explanation :

B runs 35 m in 7 sec.

B covers 200 m in
 7 35
x 200    = 40 sec.

B's time over the course = 40 sec.

A’s time over the course = (40 – 7) sec = 33 sec.

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8.
A runs 1
 3 4
times as fast as B. If A gives B a start of 60 metres. How far must the winning
post be in order that A and B reach it at the same time?
• A.
105 metres
• C.
140 metres
• B.
80 metres
• D.
45 metres
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Explanation :

Ratio of races of A and B = 7 : 4

i.e., 3 metres are gained by A in a race of 7 metres

60 metres are gained by A in a race of
 7 3
x 60    = 140 metres

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9.
P can run a kilometre in 4 minutes 50 seconds and Q in 5 minutes. By what distance can P beat Q?
• A.
30 m
•  C.33 1 m 3
•  B.16 2 m 3
•  D.26 2 m 3
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Explanation :

Here P is the winner and Q is the loser.

 Loser’s time Winner’s distance
=
 beat time + start time beat distance + start distance

 300 1000
=
 10 + 0 beat distance + 0

Beat distance =
 100 3
metres.

P beats Q by 33
 1 3
metres in 1 kilometre race.

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10.
A, B and C are three participants in one km race. If A can give B a start of 40 metres and B can give C a start of 25 metres, how many metres A can give C a start?
• A.
64 m
• C.
60 m
• B.
32 m
• D.
44 m
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Explanation :

Here A is the winner (Ist)

Since B can give C a start therefore B becomes IInd and C becomes IIIrd in the race.

(L - x12)x13 = L(x13 - x12)

(1000 - 40) x 25  = 1000 x (x13 - 40)

960 x 25  = 1000 x (x13 - 40)

(x13 - 40)  =
 96 x 25 100
= 24

x13  = 64 metres

Hence, A can give C a start of 64 metres.

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