Races and games
 A can beat B by 5 meters in 100 m and B can beat C by 15 meters in 200 m race. A can beat C in 400 m race by:

 50.5 m
 48.5 m
 45.5 m
 42.5 m

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∴ A runs 100 m while B runs 95 m
∴ A runs 400 m while B runs 95 x 400 / 100 = 380 mCorrect Option: B
∴ A runs 100 m while B runs 95 m
∴ A runs 400 m while B runs 95 x 400 / 100 = 380 m
Again, B runs 200 m while C runs 185 m
∴ B runs 380 m while C runs 185 x 200 / 380 = 3515 / 10 = 351.5 m
Hence, A runs 400 m while C runs 351.5 m
So, A can beat C by (400 – 351.5) = 48.5 m
 At a game of billiards A can give B 6 points in 50 and he can give C 13 points in 65, how many points can B give C in a game of 55?

 7
 8
 5
 10

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In a game of 50, If A scores 50 then B scores 44.
∴ A scores 65 while B 44 * 65 / 50 = 57.2 pointsCorrect Option: C
In a game of 50, If A scores 50 then B scores 44.
∴ A scores 65 while B 44 * 65 / 50 = 57.2 points
Now, B scores 57.2 points while C 52
∴ B scores 55 points while C = 52 * 55 / 57.2 = 50
Hence, in game of 55 points B can give C (55 – 50) = 5 points
 In a race of 200 metres, B can give a start of 10 metres to A and C can give a start of 20 metres to B. The start that C can give to A, in the same race, is

 30 m
 29 m
 27 m
 25 m

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B covers 200 m while A 190 m
B covers 180 m while A 190 / 200 * 180 = 171 mCorrect Option: B
B covers 200 m while A 190 m
B covers 180 m while A 190 x 180 / 200 = 171 m
Hence, C covers 200 m while A = 171 m
So, C can give to A (200 – 171) = 29 m start.
 A can run 500m in 30 seconds and B in 35 seconds. How many meter start can A give to B in a Km race so that the race may end in a deadheat?

 139^{5}⁄_{7}
 138^{5}⁄_{7}
 142^{6}⁄_{7}
 140^{5}⁄_{7}

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Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
∴ A can give B a start of (70  60) = 10 seconds.Correct Option: C
Time taken by A to run 1 Km = 30 × 2 = 60 seconds.
Time taken by B to run 1 Km = 35 × 2 = 70 seconds.
∴ A can give B a start of (70  60) = 10 seconds.
In 35 sec B runs 500 m
∴ In 10 sec B runs = 500 × 10 / 35 = 1000 / 7 = 142^{6}⁄_{7} meters
So, A can give B a start of 142^{6}⁄_{7} meters in a Km race.
 A’s speed is 1^{3}⁄_{8} times of B’s. In a race A gives B a start of 300 m. How long should the race course be so that both reach the winning post simultaneously?

 700 m
 900 m
 800 m
 850 m

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A’s speed : B’s speed = 1^{1}⁄_{2} : 1
= ^{3}⁄_{2} : 1
= 3 : 2
It means that in a race of 3 m, A gains (3  2).
= 1 m over B. 1 m is gained by A in a race of 3 m.Correct Option: B
A’s speed : B’s speed = 1^{1}⁄_{2} : 1
= ^{3}⁄_{2} : 1
= 3 : 2
It means that in a race of 3 m, A gains (3  2).
= 1 m over B. 1 m is gained by A in a race of 3 m.
∴ 300 m is gained by A in a race of = ^{3}⁄_{1} × 300 = 900 m.