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Races & Games of Skill

Important Instructions
21.

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?

Answer: B

Let the game be of x points. 

When A scores x points, B scores X – 25 points, and C scores X – 40 Points

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22.

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?

Answer: C

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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23.

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: C

No answer description available for this question.

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24.

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

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.

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25.

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

Answer: B

No answer description available for this question.

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26.

At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?

Answer: C

No answer description available for this question.

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27.

A runs 1 2/3 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

Answer: A

No answer description available for this question.

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28.

In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?

Answer: A

Let X be the length of the course

according to the question,
A beats B by 15 metres and C by 29 metres

Applying this,
If A runs X metres, B runs (X-15) and C runs ( X-29) metres.

B and C together run, B runs X metres and C runs (X-15)

=> If B runs 1 metre, C runs X-15/X

=> B runs X-15 m, C runs (X-15/x) * (X-15)

APPLYING THIS,
X-29 = (X-15)(X-15) / X

Solving,

X⊃2; -29X= X⊃2; – 30 X + 225
X = 225

Thus, length of the course is 225 metres.

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29.

If X can run 48m and Y 42m, then in a race of 1km, X beats Y by:

Answer: B

When X runs 48m, Y runs 42m.
Hence, when X runs 1000m, Y runs (1000 * 42) / 48 = 875m
X beats Y by 125m.

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30.

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?

Answer: B

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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