Races and Games

Races and Games

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Question 1
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
A
60 m
B
40 m
C
20 m
D
10 m
Question 1 Explanation: 
To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m. While A covers 3 m, B covers 4 m. While A covers 360 m, B covers ((4/3)x360)m= 480 m. Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind. A wins by 20 m.
Question 2
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
A
20 m
B
25 m
C
22.5 m
D
9 m
Question 2 Explanation: 
Distance covered by B in 9 sec. =((100/45)x9)m ==> 20 m. A beats B by 20 metres.
Question 3
In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:
A
40 sec
B
47 sec
C
33 sec
D
None of these
Question 3 Explanation: 
B runs 35 m in 7 sec. B covers 200 m in ((7/35)x200) ==> 40 sec. B's time over the course = 40 sec. A's time over the course (40 - 7) sec = 33 sec.
Question 4
In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:
A
86 sec
B
76 sec
C
80 sec
D
None of these
Question 4 Explanation: 
B runs 45/2 m in 6 sec. B covers 300 m in (6 x (2/45)x 300)sec ==> 80 sec.
Question 5
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
A
21 m
B
26 m
C
28 m
D
29 m
Question 5 Explanation: 
A : B = 100 : 75 B : C = 100 : 96. A : C =(A/B)x(B/C))==>(100/75)x(100/96)) ==>100/72= 100 : 72. A beats C by (100 - 72) m = 28 m.
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