16.
A and B run a 5 km race on a round course of 400 m. If their speeds be in the ratio 5 : 4, how often does the winner pass the other?
•  A.4 1 times 2
•  C.2 3 times 4
•  B.3 1 times 2
•  D.2 1 times 2
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Explanation :

When A makes 5 rounds, B makes 4 rounds.

In order to pass each other, the difference in number of rounds made by each must be one.
Here, A passes B each time. When A makes 5 rounds.

Distance covered by A in 5 rounds =
 5 x 400 100
= 2 km

 In covering 2 km. A passes B 1 time

In covering 5 km. A passes B =
 5 2
= 2
 1 2
times.

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17.
In a 100 m race, A runs at 5km/hr. A gives B a start of 8 m and still beats him by 8 sec. Find the speed of B
• A.
6.14 km/hr
• C.
3.14 km/hr
• B.
4.14 km/hr
• D.
2.14 km/hr
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Explanation :

Time taken by A to cover 100 m = 100 +   5 x
 5 18
= 72 sec.

B covers (100 – 8) or, 92 m in (72 + 8) or, 80 sec.

Speed of B =
 92 80
x
 16 5
= 4.14 km/hr.

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18.
A can run 20 metres while B runs 25 metres. In a km race B beats A by -
• A.
250 metres
• C.
200 metres
• B.
225 metres
• D.
125 metres
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Explanation :

In a 25 metres race B beats A by 5 metres.

In one km race B Beats A by
 5 25
x 1000    = 200 metres

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19.
A runs 1
 1 3
as Fast as B. If A gives B a start of 30 minutes. How far must be the wining post,
so that the race ends in a dead heat?
• A.
150 m
• C.
120 m
• B.
100 m
• D.
None of these
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Explanation :

Assuming L = distance of the winning post such that the race ends in a dead heat, i.e., booth the participants A and B reach the wining post at the same time.

Time taken by A = time taken by B

L
 4 3
v
 =
 L - 30 v

L = 120

Since t =
 d v
,  Where d = distance and v = speed

Length of race (distance) of wining post is 120 metres.

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20.
A can run a kilometre in 4 min. 54 sec. and B in 5 min. How many metres start can A give B in a km race so that the race may end in a dead heat?
• A.
20 metres
• C.
18 metres
• B.
16 metres
• D.
14.5 metres