## Points to Remember:

- The competitions of running, driving cars, riding on the horses or bicycles, and rowing boats, etc., are generally called
**races**. - The places like grounds, roads, rivers, lakes, etc., where races take place are called the
**race course**. - In any race, the number of participants can be 2 or more. The point from where the race starts is known as the
**starting point**. - The point at which the race ends is called the
**goal**or**winning post**. - If in a race all the participants reach the goal at the same time, the race is called
**dead heat**. Therefore,**dead heat**is that type of race which ends in a draw, i.e., no one is winner or loser. - 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 14 meters, we say that A gives B, a start of 14 meters.
- In this case, to cover a race of 100 meters, A will have to cover 100 meters while B will have to cover only (100 – 14) = 86 meters.
- In a 100 m race, ‘A can give B 14 m’ or ‘A can give B a start of 14 m’ or ‘A beats B by 14 m’ means while A runs 100 m, B runs (100 – 14) = 86 m.
- A game of 200, means that the person among the participants who scores 200 points first is the winner’.
- If A scores 200 points while B scores only 160 points, we can say that A can give B 40 points.

**Important Scenarios in a Race**

There are various mathematical statements in the various scenarios in the race. Suppose there are two participants in a race called P and Q. Between them there can be multiple scenarios as below –

Q is beaten by P by ‘x’ seconds – P finishes off the race ‘x’seconds earlier than the Q finishes the race.

Q has a start of ‘x’ seconds as compared to P – So, in this type of race P gives Q a head start of ‘x’ seconds from the starting point.

P gives Q a start of ‘a’ meters – In this race also P gives Q a head start, but this time in meters. P starts the race from starting point, while Q starts some ‘a’ meters ahead of P.

Suppose there is a race of 200 meters, then P has to cover 200 meters and Q has to cover (100 – a) meters.

So, the above scenario can also happen in a game of hundred, where P gives Q a head start of 10 or 20 points. Thus, in this race P has to get 100 points and Q has to get 80 or 90 points.

**Examples**

**Q. In a race of 200 meters, P gives Q headstart of 20 m and R 56 m. Thus, in this similar race, Q can give R a head start of how many meters?**

We can do this by using the ratio. We are given the ratio of P with reference to Q and R. So, P: Q is 200: 180 and P: R is 200: 144. Thus, Q : R will be, Q/P x P/R = 180/200 x 200/144 => 180/144. Thus, it means that when Q runs 180 meters, R will run 144 meters. So, when Q runs, R will run 144/180 x 100 = 80 m.

**Practice Questions on Race and Games of Skill**

**Q. There is a race of 224 meters which can be covered by A in 28 seconds. Similar distance is covered by B in 32 seconds. Find the distance by which A will beat B eventually.**

A. 24 m B. 32 m C. 40 m D. 44 m

Answer: B. 32 m

**Q. There is a 100 m race where P beats Q by 10 m and R by 13 m. If it is 180 m race, then Q will beat R by**

A. 4 m B. 6 m C. 7 m D. 8 m

Answer: B. 6 m