36.
In a 100 metres race. A runs at a speed of 2 metres per seconds. If A gives B a start of 4 metres and still beats him by 10 seconds, find the speed of B -
• A.
1.6 m/sec.
• C.
1 m/sec.
• B.
4 m/sec.
• D.
2.6 m/sec.
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Explanation :

Here A is the winner and B is the loser.

Loser’s time – winner’s time = beat time + start time

B’s time – A’s time = 10 + 0.

 B's distance B's speed
-
 A's distance A's speed
= 10

 (100 - 4) B's speed
-
 100 2
= 10

 96 B's speed
= 10 + 50 = 60

B's speed = 1.6 metres/sec.

Hence, the speed of B is 1.6 metres/sec.

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37.
P runs 1 km in 4 minutes and Q in 4 minutes 10 secs. How many metres start can P give Q in 1 kilometre race, so that the race may end in a dead heat?
• A.
40 m
• C.
30 m
• B.
50 m
• D.
None of these
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Explanation :

P runs 1 kilometre in 4 minutes (= 240 seconds)

Q runs a kilometre in 4 minutes 10 sec. (= 250 seconds)

P can beat Q by 10 seconds in 1 km. race

But if P gives Q a start of 10 seconds or x metres so that the race may end in a dead heat,
i.e., beat time = 0 and beat distance = 0

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

 250 1000
=
 0 + 10 0 + x

x = 40

Hence if P gives Q a start of 40 metres in a race of  one kilomere the race will end in a dead heat.

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38.
In a race of 300 m A beats B by 15 m or 5 sec. A’s time over the course is
• A.
100 sec
• C.
105 sec
• B.
95 sec
• D.
90 sec
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Explanation :

15 m is covered by B in 5 sec

300 m is covered by B in
 5 15
x 300 = 100 sec

A takes 100 - 5 = 95 sec.

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39.
In a game of 90 points A can give B 15 points and C 30 points. How many points can B give C in a game of 100 points?
• A.
140
• C.
50
• B.
20
• D.
30
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Explanation :

A : B : C = 90 : 75 : 60

B : C =
 75 60
=
70 x
 100 75
60 x
 100 75
=
 100 80

Hence, in a game of 100 points, B can give C(100 – 80) = 20 points.

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40.
A, B and C are the three constant in one km race. If A can give B a start of 40 metres and A can give C a start of 64 metres. How many metres start can B give C?
• A.
20 m
• C.
35 m
• B.
25 m
• D.
None of these
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Explanation :

While A covers 1000 metres, B covers (1000 – 40)  or 960 metres and C covers (1000 – 64) or 936 metres.

Now, when B covers 960 metres, C covers 936 metres.

When B covers 1000 metres

C covers
 936 960
x 1000    = 975 metres

So, B can give C a start of (1000 – 975) m = 25 metres.

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