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# Races & Games of Skill

1.

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

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2.

A takes 3 min 45 seconds to complete a kilometer. B takes 4 minutes to complete the same 1 km track. If A and B were to participate in a race of 2 km, how much start can A give B in terms of distance?

A can give B a start of 15 seconds in a km race.
B takes 4 minutes to run a km. i.e 1000/4= 250 m/min = 250/60 m/sec
Therefore, B will cover a distance of = 62.5 meters in 15 seconds.
The start that A can give B in a km race therefore, is 62.5 meters, the distance that B run in 15 seconds.
Hence in a 2 km race, A can give B a start of 62.5 * 2 = 125 m or 30 seconds.

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3.

If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?

When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.

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4.

In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

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5.

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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6.

In a 200m race, if A gives B a start of 25 meters, then A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 meters the race ends in a dead heat. How long does A take to run 200m?

A gives B a start of 25 meters and still wins the race by 10 seconds.
Alternatively, if A gives B a start of 45 meters, then the race ends in a dead heat.
Therefore, the additional 20 meters start given to B compensates for the 10 seconds.i.e., B runs 20 meters in 10 seconds.
Hence, B will take 100 seconds to run 200 meters.
We know that A gives B a start of 45 meters. B will take 22.5 seconds to run this 45 meters as B runs 20 meters in 10 seconds or at the speed of 2 m/s.
Hence, A will take 22.5 seconds lesser than B or 100 - 22.5 = 77.5 seconds to complete the race.

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7.

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 :

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8.

A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by :

When B runs 25 m, A runs 45/2 m.
When B runs 1000 m, A runs (45/2 *1/25 * 1000)m = 900 m.
B beats A by 100 m.

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9.

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 :

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10.

In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?

A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.

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