R. Gupta Solutions for Chapter: Races and Games, Exercise 1: EXERCISE

In a $500 m$ race, the ratio of speeds of two runners A and B is $3 : 4$. A has a start of $140 m$. Then A wins by?

In a $100 \mathrm{m}$ race, $\mathrm{A}$ runs at $6 \mathrm{km}/\mathrm{hr}$. If a gives $\mathrm{B}$ a start of $4 \mathrm{m}$ and still beats him by $12 \mathrm{s}$, what is the speed of $\mathrm{B}$?

Two men, A and B run a $4 \mathrm{km}$ race on a course $250 \mathrm{m}$ round. If their rate are $5:4$, how often does the winner pass the other: 

A runs 1.75 times as fast as B. If A gives B a start of 60 m. how far must the winning post be in order that A and B reach at the same time?

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

In a 1000 m race, A can give B 100 m and C 280 m. In the same race, B can give C?

$\mathrm{A}$ and $\mathrm{B}$ run a $\mathrm{km}$ and $\mathrm{A}$ wins by $1 \min$. $\mathrm{A}$ and $\mathrm{C}$ run a $\mathrm{km}$ and $\mathrm{A}$ wins by $375 \mathrm{m}$. $\mathrm{B}$ and $\mathrm{C}$ run a $\mathrm{km}$ and $\mathrm{B}$ wins by $30 \mathrm{s}$. Find the time taken by $\mathrm{A}$ and $\mathrm{B}$ to run a $\mathrm{km}$ race.

In a race of $300 \mathrm{m}$, $\mathrm{A}$ beats $\mathrm{B}$ by $15 \mathrm{m}$ or $5 \mathrm{s}$. $\mathrm{A}\text{'}\mathrm{s}$ time over the course is: