Races & Games of Skill Questions and Answers

Answer: C

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.

\[ A\,60 : B\,45, \qquad A\,60 : C\,40 \]

\[ B : C = 45 : 40 \]

In a game of 90, when B scores 90:

\[ C = 90 \times \frac{40}{45} = 80 \]

\[ \text{B can give C} = 90 - 80 = 10 \text{ points} \]

Both handicaps are quoted against the same A total, which is what lets B and C be compared without ever finding a speed.

Answer: A

In these problems the two players are compared by the scores they reach in the same time, so their rates are in the ratio of those scores.

The handicaps are over different totals, so scale both against A.

\[ A\,40 : B\,28 \ \Rightarrow\ B = \tfrac{7}{10}A \]

\[ A\,50 : C\,40 \ \Rightarrow\ C = \tfrac{8}{10}A \]

\[ B : C = 7 : 8 \]

C is the stronger, so in a game of 80, when C reaches 80:

\[ B = 80 \times \frac{7}{8} = 70 \]

\[ \text{C can give B} = 80 - 70 = 10 \text{ points} \]

Answer: B

P finishes in 20 seconds. In that time Q, who needs 25 seconds for 100 m, covers

\[ 100 \times \frac{20}{25} = 80 \text{ m} \]

\[ \text{P beats Q by } 100 - 80 = 20 \text{ m} \]

Answer: B

Correct answer: 20 m

With a 140 m start, A has only \(500 - 140 = 360\) m to run. In the time A covers that,

\[B \text{ covers } 360 \times \frac{4}{3} = 480 \text{ m}\]

B still has \(500 - 480 = 20\) m to go when A finishes, so A wins by 20 m.

Answer: B

Since A beats B by 60 seconds and B beats C by 30 seconds. So, A beats C by 90 seconds. But, it being given that A beats C by 375 metres. So it means that Covers 375 metres in 90 seconds.
Time taken by C to cover 1 km =90/375×1000 seconds= 240 seconds
Time taken by A to cover 1 km = (240-90) seconds = 150 seconds
Time taken by B to cover 1 km = (240-30) seconds= 210 seconds.

Answer: C

A starts 140 m ahead, so A has only 360 m to cover while B has the full 500 m.

Speeds are in the ratio 3 : 4, so in the time A covers 360 m:

\[ \text{B covers } 360 \times \frac{4}{3} = 480 \text{ m} \]

\[ \text{A wins by } 500 - 480 = 20 \text{ m} \]

The head start is subtracted from A's distance, not added to B's.

Answer: B

When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.

Answer: B

Correct answer: 50 m

From the first race, A : B = 200 : 175 = 8 : 7.

When A covers 400 m, B covers

\[400 \times \frac{7}{8} = 350 \text{ m}\]

So A wins by \(400 - 350 = 50\) m. The margin doubles because the course has doubled.

Answer: B

This is a simple speed time problem. Given conditions:

=>Speed of P= 224/28 = 8m/s

=>Speed of Q=224/32 = 7m/s

=>Difference in time taken = 4 seconds

Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres

Answer: B

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.

\[ A\,200 : B\,169, \qquad A\,200 : C\,182 \]

\[ C : B = 182 : 169 \]

In a 350 m race, when C finishes:

\[ B = 350 \times \frac{169}{182} = 325 \text{ m} \]

\[ \text{C beats B by } 350 - 325 = 25 \text{ m} \]