Races and Games Questions and Answers

Exercise


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Q 1

In a 500 m race, A beats B by 40 metres or 8 seconds. Find A's time over the course.


A)  

100 s

B)  

92 s

C)  

108 s

D)  

98 s


Correct Option - B

Explanation

B covers 40 meters in 8 seconds.

B's speed = 40/8 = 5 m/s

Time taken by B to cover 500m

= 500/5

= 100 seconds

A beats B by 8 seconds. Hence,

Time taken by A

= 100-8

= 92 seconds

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Q 2

A and B take part in a 100 m race. A gives B a start of 10 m and still beats B by 5 seconds. If A's speed is 2.5 m/s, find B's speed.


A)  

2 m/s

B)  

2.5 m/s

C)  

1.5 m/s

D)  

2.25 m/s


Correct Option - A

Explanation

Time taken by A to cover 100 m

= 100/2.5

= 40 seconds

A gives B a start of 10 m. Hence, B covers only 90 m.

A beats B by 5 seconds.

Hence, time taken by B to cover 90 m

= 40+5

= 45 seconds

B covers 90 m in 45 seconds.

B's speed

= 90/45

= 2 m/s

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Q 3

A's speed is twice B's speed. In a 100m race, how many metres start can A give B so that the race ends in a dead heat?


A)  

50 m

B)  

25 m

C)  

10 m

D)  

75 m


Correct Option - A

Explanation

For the race to end in a dead heat,

both A and B should reach the winning post at the same time.


A's speed is twice B's speed.


To run the same distance,

time taken by B=2*(time taken by A)

Time taken by B to run 100 m

= 2*Time taken by A to run 100 m

Time taken by B to run 50 m

= Time taken by A to run 100 m

Hence, A can give B a start of 50 m.

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Q 4

The speeds of A and B are in the ratio 3:4. B gives A a start of 30 m. How far should the winning post be so that the race ends in a dead heat?


A)  

100 m

B)  

200 m

C)  

150 m

D)  

120 m


Correct Option - D

Explanation

Let A's speed be 3x m/s and

     B's speed be 4x m/s

Let the distance of the winning post be l m.

Time taken by A to finish the race

= (l-30)/3x

Time taken by B to finish the race

= l/4x

For the race to end in a dead heat,

(l-30)/3x = l/4x

Solving,

l = 120 m

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Q 5

Ram and Lakshman take part in a 200 m race. Ram beats Lakshman by 15 seconds. If Ram's speed is 2 m/s, find the time taken by Lakshman to finish the race.


A)  

115 seconds

B)  

100 seconds

C)  

85 seconds

D)  

105 seconds


Correct Option - A

Explanation

Time taken by Ram to finish

= 200/2

= 100 seconds

Ram beats Lakshman by 15 s.

Time taken by Lakshman to finish

= 115 seconds

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Q 6

P can run a 500 m race in 3 minutes and Q in 3 mins 20 seconds. How many meters start can P give Q so that the race ends in a dead heat?


A)  

50 m

B)  

40 m

C)  

25 m

D)  

20 m


Correct Option - A

Explanation

Q takes 20 seconds more than P to run 500 m

Distance covered by Q in 3 mins 20 seconds(200 s)

= 500m

Distance covered by Q in 20 seconds

= (500/200)*20

= 50 m

If Q skips 50m, the race can be finished in 3 minutes(same as P).

Hence, for the race to end in a dead heat,

P should give Q a start of 50 m.

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Q 7

In a race, A beats B by 20 m or 10 seconds. Find B's speed.


A)  

4 m/s

B)  

5 m/s

C)  

2 m/s

D)  

2.5 m/s


Correct Option - C

Explanation

20 meters are covered by B in 10 seconds.

B's speed

= 20/10

= 2 m/s

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