Clocks
October 5, 2022
Problems on Numbers
October 5, 2022About this post
Welcome! The aim of this topic is to help you solve the various kinds of problems on Races and Games. The first lesson in this topic is an introduction to Races and Games where we have shared some important points and terminologies involved . The exercises contain solved question and answers on Races and Games. When solving exercises, we recommend you to try solving the problems on your own, then view the solution.
By the end of this post, you will learn to solve the following types of problems:
- A and B are two friends who plan to run a race of X mts. B being slow, A gives B a lead of y mts. Now if you know the speed of A can you find the speed of B?
- In the above problem, if you know the speeds of A and B and lead given by A to B, can you find the length of the race.
- In a game of m points. If A gives B x points and B gives C y points. How many points can A give C
Introduction to Races
Starting Point: The point from which the race begins is the starting point.
Winning Point (or Goal): The point where the race ends is the winning point or goal.
Dead Heat: If all the contestants in a race reach the ending point at exactly the same time, then the race is said to end in dead heat.
In a race between 2 contestants A and B,
- If A gives B a start of ‘x’ metres, then A is at the starting point and B is ahead of A by ‘x’ metres.
- If A beats B by ‘x’ metres, say, in a 100m race, then while A runs 100 metres B runs 100-x metres.
- If A gives B a start of ‘t’ seconds, then A starts ‘t’ seconds after B starts from the same starting point.
- If A beats B by ‘t’ seconds, then A finishes the race ‘t’ seconds before B
Note : From the above points we see that, for a race of 100 metres the following statements are equivalent – “A beats B by 10 metres” or “A gives B a start of 10 metres’ or “A can give B a start of 10 metres”
Introduction to Games
In a game of 100, if A scores 100 points first, then A is the winner.
In a game of 100, If A gives B 10 points, it implies that when A scores 100 points, B scores 90 points.
