Races- A contest of speed in running, riding, driving sailing or rowing is called a race. The ground of path on which contexts are made is called a race course. The point from which a race begins is known as a starting point. The point set to bound a race is called a winning post or a goal. The person who first reaches the winning post is called a winner. 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.

Suppose A and B are two contesting in a race. If both the start of the race, A is at the starting point and B is ahead of A by 15 metres. To cover a race of 200 metres in this case A will have to cover a distance of 200 metres and B will have to cover (200-15) or 185 metres only.
In a 100 metres race A can give B 15 metres or A can give B, a start of 15 metres means or A beats B by 15 metres means that while A runs 100 metres, B runs (100-15) or 85 metres.

Games- A games 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.

Races and Games Aptitude Questions and Solutions

Question 1. A and B run a km and A wins by 1 minute. A and C run a km and ‘A’ wins by 375 metres. B and C run a km and B wins by 30 seconds. Find the time taken by each to run a km.

Solution: 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.
$\therefore$ Time taken by C to cover 1 km
=$\frac{90}{375}\times 1000$ 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.

Question 2. In a kilometer race, If A gives B, a start of 40 metres, then A wins by 19 seconds, but if A gives B, a start of 30 seconds then B wins by 40 metres. Find the time taken by each to run a kilometre.

Solution: Suppose that the time taken by A and B to run 1 km is x and y seconds respectively.
When A gives B a start of 40 metres then A has run 1000 metres, while B has to run only 960 metres.
Time taken by A to run 1000 m = x sec.
Time taken by B to run 960 metres = $\left ( \frac{y}{100}\times 960 \right )$ sec.
= $\left ( \frac{24}{25} y\right )$ sec.
Clearly, $\because \left ( \frac{24}{25}\right )$ y-x = 19
$\Rightarrow$ 24y – 25x = 475 ……(i)
Again, A gives B, a start of 30 seconds, then B runs for y seconds, while A runs for (y-30) seconds.
Now, $\because$ In x seconds, A covers 1000 metres.
$\therefore$ In (y-30) seconds A will cover = $\left [ \frac{100}{x} \times (y-30)\right ]$ metres.
So, $1000-\frac{1000\times (y-30)}{x}$ = 40
$\Rightarrow$ 25y-24x = 750…..(ii)
Solving (i) and (ii) we get,
X = 125 and y = 150
$\therefore$ Time taken by A to run 1 km = 125 seconds
Time taken by B to run 1 km = 150 seconds

Question 3. A can run a kilometre in 4 minutes 50 seconds and B in 5 minutes. How many metres start can A give B in a kim race, So that the race may and in a dead heat.

Solution: Time taken by A to run 1 km = 4 mts. 50 sec. = 290 sec.
Time taken by B to run 1 km = 5 mts. = 300 sec.
$\therefore$ A can give B, a start of (300-290) or 10 second
Now, in 300 seconds, B runs 1000 meters.
$\therefore$ In 10 seconds, B runs
$\left ( \frac{1000}{300}\times 10 \right )m\: =\: 33\frac{1}{3}\: m$
So, A can give B a start of $33\frac{1}{3}$ metres.

Question 4. In a 100 metres race, A runs with 6 kms. Per hour. If A gives B a start of 4 metres and still beats him by 12 seconds. What is the speed B ?

Solution: Time taken by A to cover 100 metres
= $\left ( \frac{60\times 60}{6000}\times 100 \right )\: seconds$
= 60 seconds
$\therefore$ B covers (100-4) or 96 m in (60+12) sec. or 72 sec,
Hence, speed of B
= $\left ( \frac{60\times 60\times 60}{72\times 1000} \right )\: km/hr.$
= 4.8 km/hr.

Question 5. A can run a km in 3 min. 10 sec. and B in 3 min. 20 sec. By what distance can A beat B ?

Solution: $\because$ A beats B by 10 seconds.
Distance covered by B in 200 seconds = 1000 metres.
Distance covered by B in 10 seconds = $\frac{1000}{200}\times 10$
= 50 metres
$\therefore$ A beats B by 50 metres.

Races and Games Aptitude Questions from Previous Year Exams

Races and Games Video Lecture