Races & Games of Skill Questions and Answers

Q: In a 100 m race, A beats B by 20 m. What is the ratio of their speeds ?

Correct answer: 5 : 4In the time A covers 100 m, B covers only 80 m, and both run for the same length of time.\[\text{Speed ratio} = 100 : 80 = 5 : 4\]Speeds are in the ratio of the distances covered in equal times, which is why the beaten distance is subtracted from the full course.

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81.

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

A.100 m
B.111m
C.25 m
D.50 m

Answer: A

In these problems the two runners are compared by the distances they cover in the same time, so their speeds are in the ratio of those distances.

\[ A : B = 22.5 : 25 \]

In a 1000 m race B finishes first, and A has then covered

\[ 1000 \times \frac{22.5}{25} = 900 \text{ m} \]

\[ \text{B beats A by } 1000 - 900 = 100 \text{ m} \]

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82.

In a 100 m race, P can give Q 20 m and R 32 m. In the same race Q can give R:

A.19 m
B.22 m
C.15 m
D.10 m

Answer: C

P : Q = 100 : 80.
P : R = 100 : 68.
Q : R = Q/P * P/R
= (80/100) * (100/68)
= 80/68
When Q runs 80 m, R runs 68 m.
When Q runs 100 m, R runs ((68/80) * 100)m = 85m
Q can give R 15 m.

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83.

In a 100 m race, A beats B by 20 m. What is the ratio of their speeds ?

A.4 : 5
B.5 : 4
C.3 : 2
D.2 : 1

Answer: C

Correct answer: 5 : 4

In the time A covers 100 m, B covers only 80 m, and both run for the same length of time.

\[\text{Speed ratio} = 100 : 80 = 5 : 4\]

Speeds are in the ratio of the distances covered in equal times, which is why the beaten distance is subtracted from the full course.

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84.

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

A.40 points
B.14 points
C.10 points
D.8 points

Answer: C

In a game of 100 points, A scores 100 points, B scores (100-20)=80 points and C scores (100-28)=72 points
i.e., when B scores 80 points, C scores 72 points
When B scores 100 points, C scores 72/80×100 = 90 points
i.e., In a game of 100 points, B can give C (100-90)=10 points

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85.

A runs 1 3/4 times as fast as B. If A gives B a start of 60 meters. How far must the winning post be in order that A and B reach it at the same time?

A.105 metres
B.140 meters
C.80 meters
D.45 meters

Answer: B

A is \( 1\tfrac{3}{4} = \tfrac{7}{4} \) times as fast as B, and B starts 60 m ahead. Let the post be \( d \) metres away.

\[ \frac{d}{7/4} = \frac{d - 60}{1} \]

\[ 4d = 7d - 420 \quad\Longrightarrow\quad 3d = 420 \]

\[ d = 140 \text{ m} \]

Checking: A runs 140 m while B runs 80, and \( \tfrac{140}{80} = \tfrac{7}{4} \).

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86.

In a 550 m race, the ratio of the speeds of two contestants P and Q is 3 : 4. P has a start of 170 m. Then, P wins by:

A.50 m
B.44 m
C.25 m
D.15 m

Answer: B

To reach the winning post A will have to cover a distance of (550 - 170)m, i.e., 380 m.
While P covers 3 m, Q covers 4 m. (380 * (4/3)) = 506
While P covers 440 m, Q covers
Thus, when P reaches the winning post, Q covers 506 m and therefore remains 44 m behind.
P wins by 44 m.

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87.

In a game of 100 points, A can give B 20 points and C 28 points. Number of points B can give C in a game of 100 points is

A.10
B.15
C.90
D.85

Answer: A

In these problems the two runners are compared by the distances they cover in the same time, so their speeds are in the ratio of those distances.

\[ A\,100 : B\,80, \qquad A\,100 : C\,72 \]

\[ B : C = 80 : 72 \]

In a game of 100, when B scores 100:

\[ C = 100 \times \frac{72}{80} = 90 \]

\[ \text{B can give C} = 100 - 90 = 10 \text{ points} \]

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