Races & Games of Skill Questions and Answers

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:

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

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

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

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

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

Answer: C

Chain the two comparisons through B.

\[ A\,100 : B\,75, \qquad B\,100 : C\,96 \]

When A runs 100, B runs 75; and when B runs 75, C runs

\[ 75 \times \frac{96}{100} = 72 \text{ m} \]

\[ \text{A beats C by } 100 - 72 = 28 \text{ m} \]

The two margins do not simply add to 29 - B's 4 m lead over C is measured over 100 m, but B only runs 75 m in this race.

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.

\[ A\,60 : B\,40, \qquad A\,60 : C\,30 \]

\[ B : C = 40 : 30 = 4 : 3 \]

In a game of 100, when B scores 100:

\[ C = 100 \times \frac{3}{4} = 75 \]

\[ \text{B can give C} = 100 - 75 = 25 \text{ points} \]

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.

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.

Answer: B

"By 50 m or 10 seconds" means B needs 10 seconds for that final 50 m.

\[ v_{B} = \frac{50}{10} = 5 \text{ m/s} \]

\[ t_{B} = \frac{1000}{5} = 200 \text{ s} \]

\[ t_{A} = 200 - 10 = 190 \text{ s} \]

The question asks for A's time, so the 10 seconds must be subtracted from B's.

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.

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

\[ B : C = 80 : 72 \]

In a game of 100, when B scores 100:

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

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

Answer: A

"A can give B 10 m".
In a 100 m race, while A starts from the starting point, B starts 10 meters ahead from the same starting point at the same time.
"A can give C 28 m"
In a 100 m race, while A starts from the starting point, C starts 28 meters ahead from the same starting point at the same time.
i.e., in a 100-10=90 m race, B can give C 28-10=18 m
In a 100 m race, B can give C 18/90×100 = 20 m

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