Races and games
- 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?
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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 500 m race, the ratio of 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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To reach the winning post, A will have to cover a distance of (500 - 140). i.e , 360 m.
While A covers 3 m, B covers 4 m.Correct Option: C
To reach the winning post, A will have to cover a distance of (500 - 140). i.e, 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers 4 × 360 / 3 = 480 m.
So, A reaches the winning post while B remains 20 meter behind.
∴ A wins by 20 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?
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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.
- 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?
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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.
- Two boys, A and B, runs at 41⁄2 and 6 Km an hour. A having 190 m start. The course being 1 Km, B wins by a distance of :
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Speeds (in m/sec) of A and B are
9 / 2 * 5 / 18 = 5 / 4 and 6 * 5 / 18 = 5 / 3, respectively.Correct Option: A
Speeds (in m/sec) of A and B are
9 / 2 * 5 / 18 = 5 / 4 and 6 * 5 / 18 = 5 / 3, respectively.
A has a start of 190 m.
So, A has to run 1000 - 190 = 810 m, while B 1000 m.
Time taken by B to cover 1000 m = 3 5 × 1000 = 600 seconds.
In this time, A covers 5 × 600 / 4 = 750 m.
So, B reaches the winning post while A remains 810 - 750 = 60 m behind.
∴ B wins by 60 m.
