# Races and Games Questions

FACTS  AND  FORMULAE  FOR  RACES  AND  GAMES  QUESTIONS

1. Races : A contest of speed in running, riding, driving, sailing or rowing is called a race.

Race Course : The ground or path on which contents are made is called a race course.

Starting Point : The point from which a race beigns is known as a starting point.

Winning Point or Goal : The point set to bound a race is called a winning point or a Goal.

Winner : The person who first reaches the winning point is called a winner.

Dead Heat Race : If all the persons contesting a race reach the goal exactly at the same time, then the race is said to be a dead heat race.

Start : Suppose A and B are two contestants in a race. If before the start of the race, A is at  the starting point and B is ahead of A by 12 metres, then we say that 'A gives B, a start of 12 metres'.

To cover, a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 - 12) = 88 metres.

In a 100m race, 'A can give B 12m' or 'A can give B a start of 12m' or 'A beats B by 12m' means that while A runs 100m, B runs (100-12)=88m

2. Games : A game of 100, means that the person among the contestants who scores 100 points first is the winner?

If A scores 100 points while B scores only 80 points, then we say that 'A can give B 20 points'.

Q:

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

 A) 20m B) 25m C) 22.5m D) 9m

Explanation:

Distance covered by B in 9 sec. = $\inline&space;\fn_jvn&space;{\color{Black}&space;\left&space;(&space;\frac{100}{45}\times&space;9&space;\right&space;)m}$ = 20m

$\fn_jvn&space;{\color{Black}&space;\therefore&space;}$ A beats B by 20 metres.

7 7565
Q:

In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

 A) 5.4m B) 4.5m C) 5m D) 6m

Explanation:

A : B = 100 : 90.

A : C = 100 : 87.

$\inline&space;\fn_jvn&space;{\color{Black}\therefore&space;\frac{B}{C}=\left&space;(&space;\frac{B}{A}&space;\times&space;\frac{A}{C}\right&space;)=\left&space;(&space;\frac{90}{100}\times&space;\frac{100}{87}&space;\right&space;)=\frac{30}{29}}$

When B runs 30 m, C runs 29 m.

When B runs 180 m, C runs $\inline&space;\fn_jvn&space;{\color{Black}\left&space;(&space;\frac{29}{30}&space;\times&space;180\right&space;)m}$=174m

$\inline&space;\fn_jvn&space;{\color{Black}\therefore&space;}$ B beats C by (180 - 174) m = 6 m.

5 6557
Q:

In a 1 km race, A beats B by 28 meters in 7sec. Find A's time over the course?

 A) 5min,4sec B) 4min,3sec C) 2min,3sec D) 3min,4sec

Explanation:

B covers 28 meters in 7sec. So, B's time over the course = $\inline \fn_cm \frac{7}{28}\times 1000$=250 sec.

Whereas A's time over the course = 250 -7 = 243 sec.

i.e A's time over the course is 4min , 3 sec.

8 5452
Q:

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?

 A) 30 points B) 20 points C) 10 points D) 12 points

Explanation:

A : B = 60 : 45.

A : C = 60 : 40.

$\inline&space;\fn_jvn&space;{\color{Black}\therefore&space;\frac{B}{C}=\left&space;(&space;\frac{B}{A}&space;\times&space;\frac{A}{C}\right&space;)=\left&space;(&space;\frac{45}{60}\times&space;\frac{60}{40}&space;\right&space;)=\frac{45}{40}=\frac{90}{80}=90:80}$

B can give C 10 points in a game of 90.

8 4525
Q:

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:

 A) 22.75 m B) 25 m C) 19.5 m D) 18.5 m

Explanation:

A : B = 200 : 169.

A : C = 200 : 182.

$\inline&space;\fn_jvn&space;{\color{Black}&space;\frac{C}{B}=\left&space;(&space;\frac{C}{A}\times&space;\frac{A}{B}&space;\right&space;)=\left&space;(&space;\frac{182}{200}\times&space;\frac{200}{169}&space;\right&space;)=182:169}$

When C covers 182 m, B covers 169 m.

When C covers 350 m, B covers $\inline&space;\fn_jvn&space;{\color{Black}\left&space;(&space;\frac{169}{182}\times&space;350&space;\right&space;)m}$ = 325 m

Therefore, C beats B by (350 - 325) m = 25 m.