Shortcut - Races and Games
IMPORTANT TERMS:
(i) Race: A competition in running, riding, swimming, cycling etc.
(ii) Race Course: The plane on which competitions of races are contested.
(iii) Starting Point: The point from which the race starts .
(iv) Winning Point (Post) : The last point at which race is completed.
(v) Dead Heat: A contest of race in which all the competitors set the same time and no one is winner.
(vi) A Game of Hundred: A game in which the players agree that whoever first score hundred points is the winner.
(vii) while A scores 100 points, B scores only 75 points, then we say that 'In a game of 100 A can give B 25 points'.
(viii) In a race of 100 metres A beats B by 20 metres, means while A runs 100 metres B runs 80 metres.
Question:
Two men A and B walk around a circle 1500 metres in circumference. A walks at the rate of 140 metres, and B at the rate 80 metres per minute .if they start from the same point, and walk in the same direction, when will they be together again?
Answer:
Question:
A and B run a km race A wins by 1 minute. A and C run a km race and A wins by 375 metres. B and C run a km race and B win By 30 seconds.Find the time that C takes to run a km race.
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Question:
In a game of Snooker, A can Give B 16 Points in 80 and A can Give C 15 point in 90. How many points can C give B in a game of 50?
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Question:
In a 2 Km race, P can give Q 200 m and R 560 m. In the same race, Q can give R
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Question:
A can give B 25 point, A can give C 40 points and B can give C 20 Points. How many points make the game?
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Question:
In a game of billiards, A can give B 10 points in 60 and he can give C 15 in 60.How many points can B give C in a game of 90?
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Question:
A can run 1 km in 5 minutes 48 seconds and B in 6 minutes. How many metres start can A give B in 1 km race so that the race may end in a dead heat?
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Question:
At a game of billiard, A can give B 12 points in a game of 40 and A can give C 10 Points in game of 50. How many points can C and B in a game of 80?
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Question:
In a race of 800 m, A can beat B by 74 m and in a race of 600 m, B beat C by 50 m. By how many metres will A beat C in a race of 500 m?
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Question:
A can gives B 40 points, A can give C 64 points, and B can give C 30 points.How many points to make the game?
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Question:
Two men, A and B run a 10 km race on a course 400 m round.If their rates are 5: 4, how often does the winner pass the other?
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Question:
Three girls Seema, Kiran and Nitu walk around a circle 3 km in circumference at the rates of 200, 150 and 125 metres per minute respectively. if they all start together and walk in the same direction, when will they first be together again?
Answer:
Question:
A and B start from the same point and travel in the same direction around a circular track 3 km in circumference, If their speed is 200 and 150 metres a minute, when will they first together again at the starting point?
Answer:Time taken by A in one round =$\dfrac{3000}{200}$=15 minutes.
Time taken by B in one round =$\dfrac{3000}{150}$=20minutes.
L.C.M of 15 min and 20 min =60min =1hour.
Hence,they will meet first together at the starting point after 1 hour.
Question:
Two men, A and B run a 500 m race, A having 140 m start their speeds are 3 :4. Then, A wins By:
Answer:Here, greatest have to cover a distance of ( 500-140) = 360 m to reach the winning point while B 500 m Now, A covers 3m while B covers 4 m
A covers 360 m while B covers 4/3 x 360 = 480 m
Hence, B will be ( 500- 480) = 20 m behind the winning post.
A wins by 20 min.
Question:
A runs 1.5 Times as fast as B can. If A gives B a start of 50 m, how far must the winning post be in order that A and B reach at the same time
Answer:
Question:
in a race of 200 metres, A can give a start of 10 metres to A C give a start of 20 metres to B. The start that C can give to A, in the same race is
Answer:B covers 200 m while A 190 m
B covers 180 m while A 190/200x180 = 171 m
Hence, C covers 200 m while A = 171 m
So, C can give to A ( 200 - 171) = 29 m Start.
Question:
P and Q run a Kilometers and P win by 1 minutes. P and R run a kilometre and P wins by 375 m. Q and R run a kilometre and Q wins By 30 Seconds. Find the time taken by each runner to run a kilometre.
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Question:
P can run 100m in 20 second and Q in 25 seconds. P beats Q by
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Question:
In a race of 300 metres A rates B by 15 metres or 5 seconds, Hoe much time A take to complete the race?
Answer:From the question it is clear that speed of B = 15/5 = 3 m/s
the time taken by B to cover 300 m = 300 / 3 = 100 sec.
Hence, Time taken by A to complete the race = 100-5 = 95 sec.
Question:
A is 1 $\dfrac{3}{5}$ times quicker than B. If A gives B a Start of 75 meters, Find the length of racecourse so that both of them reach the winning post at the same time.
Answer: