Aptitude:: Races and Games: Ques1

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Aptitude :: Races and Games

Ques1: In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
A. 18 m
B. 20 m
C. 27 m
D. 9m
Answer: Option B
Explanation:
A : B = 100 : 90.
A : C = 100 : 72.
B A 90 100 90
B:C= x = x = .
A C 100 72 72
When B runs 90 m, C runs 72 m.
72
When B runs 100 m, C runs x 100 = 80 m.
90 m
B can give C 20 m.
Ques2: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and
still beats him by 8 seconds. The speed of B is:
A. 5.15 kmph
B. 4.14 kmph
C. 4.25 kmph
D. 4.4 kmph
Answer: Option B
Explanation:
5 25
A's speed = 5x = m/sec.
18 m/sec 18
18
Time taken by A to cover 100 m = 100 x = 72 sec.
25 sec
Time taken by B to cover 92 m = (72 + 8) = 80 sec.

92 18
B's speed = x = 4.14 kmph.
80 5 kmph
Ques3: 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:
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A. 60 m
B. 40 m
C. 20 m
D. 10 m
Answer: Option C
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.
4
While A covers 360 m, B covers x 360 = 480 m.
3 m
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m.
Ques4: In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat
C by:
A. 5.4 m
B. 4.5 m
C. 5m
D. 6m
Answer: Option D
Explanation:
A : B = 100 : 90.
A : C = 100 : 87.
B B A 90 100 30
= x = x = .
C A C 100 87 29
When B runs 30 m, C runs 29 m.
29
When B runs 180 m, C runs x 180 = 174 m.
30 m
B beats C by (180 - 174) m = 6 m.
Ques5: At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in
60. How many points can B give C in a game of 90?
A. 30 points
B. 20 points
C. 10 points
D. 12 points

Answer: Option C
Explanation:
A : B = 60 : 45.
A : C = 60 : 40.
B B A 45 60 45 90
= x = x = = = 90 : 80.
C A C 60 40 40 80
B can give C 10 points in a game of 90.
Ques6:In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will
beat B by:
A. 22.75 m
B. 25 m
C. 19.5 m
D. 7m
Answer: Option B
Explanation:
A : B = 200 : 169.
A : C = 200 : 182.
C C A 182 200
= x = x = 182 : 169.
B A B 200 169
When C covers 182 m, B covers 169 m.
169
When C covers 350 m, B covers x 350 = 325 m.
182 m
Therefore, C beats B by (350 - 325) m = 25 m.
Ques7: 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. 9m
Answer: Option A
Explanation:
100
Distance covered by B in 9 sec. = x9 = 20 m.
45 m
A beats B by 20 metres.

Ques8: In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give
C:
A. 8 points
B. 10 points
C. 14 points
D. 40 points
Answer: Option B
Explanation:
A : B = 100 : 80.
A : C = 100 : 72.
B B A 80 100 10 100
= x = x = = = 100 : 90.
C A C 100 72 9 90
B can give C 10 points.
Ques9: 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
Answer: Option C
Explanation:
B runs 35 m in 7 sec.
7
B covers 200 m in x 200 = 40 sec.
35
B's time over the course = 40 sec.
A's time over the course (40 - 7) sec = 33 sec.
Ques10: A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
A. 100 m
B. 110 m
C. 25 m
D. 50 m
Answer: Option A
Explanation:
45
When B runs 25 m, A runs m.
2
When B runs 1000 m, A runs 45 x 1 x 1000 = 900 m.
m
2 25
B beats A by 100 m.
Ques11: 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. 80 sec
C. 76 sec
D. None of these
Answer: Option B
Explanation:
45
B runs m in 6 sec.
2
2
B covers 300 m in 6x x 300 = 80 sec.
sec
Ques12: A runs 1 1/2 times as fast as B. If A gives B a start of 80 m, how far must the
winning post be so that A and B might reach it at the same time?
A. 200 m
B. 300 m
C. 270 m
D. 160 m
Answer: Option A
Explanation:
5
Ratio of the speeds of A and B = : 1 = 5 : 3.
3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
5
80 m will be gained by A in race of x 80 = 200 m.
2 m
Winning post is 200 m away from the starting point.
Ques13: 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
Answer: Option C

Explanation:
A : B = 100 : 75
B : C = 100 : 96.
A B 100 100 100
A:C= x = x = = 100 : 72.
B C 75 96 72
A beats C by (100 - 72) m = 28 m.

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Aptitude :: Races and Games

Time taken by B to cover 92 m = (72 + 8) = 80 sec.

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