Races and games
 In a game of 80 points, A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?

 12
 10
 8
 6

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In a Game of 80 points,
A scores 80 points , B scores 75 points and C scores 65 points.
∵ B scores 75 points while A 80
∴ B scores 60 points while A = 80 x 60 / 75 = 64Correct Option: C
∵ B scores 75 points while A 80
∴ B scores 60 points while A = 80 x 60 / 75 = 64
Again, A scores 80 points while C = 65
∴ A scores 64 points while C = 65 x 64 / 80 = 52 points
Hence, in a game of 60, B can give C (60 – 52) = 8 points
 Two men A and B run a 500 m race, A having 140 m start, their speeds are as 3 : 4. Then, A wins by :

 10 m
 20 m
 40 m
 60 m

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Here, A will have to cover a distance of (500 – 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4.
Correct Option: B
Here, A will have to cover a distance of (500 – 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4.
∴ A covers 360 m while B covers 4 x 360/ 3 = 480 m
Hence, B will be (500 – 480) = 20 m behind the winning post.
∴ A wins by 20 m.
 In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meters will A beat C in a race of 400 m?

 364 m
 254 m
 324 m
 354 m

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Clearly, if A runs 600 meters, B runs = 540 m.
Correct Option: C
Clearly, if A runs 600 meters, B runs = 540 m.
∴ If A runs 400 m, B runs = 540 x 400 / 600 = 540 x 4 / 6 = 90 x 4 = 360 m
Again, when B runs 500 m, C runs = 450 m
∴ When B runs 360 m, C runs = 450 x 360 / 500 = 45 x 36 / 5 = 9 x 36 = 324 m.
∴ A beats C by 400  324 = 76 m.
 In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meter will A beat C in a race of 400 m?

 78 m
 56 m
 76 m
 86 m

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If A runs 600 m, B runs 600  60 or, 540 m.
If A runs 400 m, B runs = 540 x 400 / 600 = 360 m.
Now, when B runs 500 m, C runs 500  50 = 450 m.Correct Option: C
If A runs 600 m, B runs 600  60 or, 540 m.
If A runs 400 m, B runs = 540 x 400 / 600 = 360 m.
Now, when B runs 500 m, C runs 500  50 = 450 m.
∴ When B runs 360 m, C runs = 450 * 360 / 500 = 324 m
∴ A beats C by 400  324 = 76 m.
 In a game A can give B 25 points in 75 and C 18 points in 90. How many points can C give B in a game of 120?

 20
 30
 40
 50

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When A scores 75 points, B scores 50 points.
When A scores 90 points, C scores (90  18) = 72 points.
∴ When A scores 75 points, C scores = 72 × 75 / 90 = 60 points.Correct Option: A
When A scores 75 points, B scores 50 points.
When A scores 90 points, C scores (90  18) = 72 points.
∴ When A scores 75 points, C scores = 72 × 75 / 90 = 60 points.
A : B : C = 75 : 50 : 60
C : B = 60 / 50 = 120 / 100
So, in a game of 120, C can give B
(120  100) = 20 points.