**IMPORTANT FACTS**

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

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

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

**Winning Point or Goal:**The point set to bound a race is called a winning paint 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 100 m race, ‘A can give B 12 m’ or ‘A can give B a start of 12 m’ or ‘A beats 12 m’ means that while A runs 100 m, B runs (100 – 12) = 88 m.

**Games**: ‘A game of 100, means that the person among the contestants who scores 100m 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.

**SOLVED EXAMPLES:**

1. In a km race, A beats B by 28 metres or 7 seconds. Find A’s time over the course.(243s)

2. A runs 1 ¾ times as fast as B. if A gives B a start of 84 m, how far must winning post be so that A and B might reach it at the same time? (196)

3. A can run 1 km in 3 min. 10 sec. and B can cover the same distance in 3 min. 20 sec. By what distance can A beat B? (50 metres)

4. In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B? (5.76kmph)

5. A, Band C are three contestants in a km race. If A can give B a start of 40 m and A can give C a start of 64m how many metres start can B give C? (25 metres)

6. In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60? (8 points)

**EXERCISE**

1. In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by : (20 metres)

2. In a 200 metres race A beats B by 35 m or 7 seconds. A’s time over the course is : (33s)

3. In a 300 m race A Beats B by 22.5 m or 6 seconds. B’s time over the course is : (80s)

4. A can run 22.5 m while B runs 25 m. In a kilo metre race B beats A by : (100 metres)

5. In a 500 m race, the ratio of the speeds of two contestants A and B is 3: 4. A has a start of 140 m. Then, A wins by : (20 metres)

6. A runs 1 2/3 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time? (200 metres)

7. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by : (28 metres)

8. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C : (20m)

9. In a 100 m race, A beats B by 10 m and C by C by 13 m. In a race of 180 m, B will beat C by: (6 m)

10. 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 : (25 metres)

11. A and B take part in a 100 m race. A runs at 5km per hour. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is: (4.14kmph)

12. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C :(10)

13. At a game of billiards, A can give B 15 points in 60 and A can give C 20 points in 60. How many points can B give C in a game of 90? (10)