R. S. Aggarwal Solutions for Chapter: Races and Games of Skill, Exercise 1: Exercise 31

A can run $100 \mathrm{m}$ in $35$ seconds and $\mathrm{B}$ in $40$ seconds. A beats B by

In a $200 \mathrm{m}$ race, $\mathrm{A}$ beats $\mathrm{B}$ by $10$ metres or $5$ seconds. A's time over the course is:

A can run $22 \mathrm{m}$ while $\mathrm{B}$ runs $25 \mathrm{m}.$ In a $\mathrm{km}$ race, $\mathrm{B}$ beats $\mathrm{A}$ by:

A can run $1 \mathrm{km}$ in $4 \min 54\sec$ and $\mathrm{B}$ in $5 \min .$ How many metres' start can $\mathrm{A}$ give $\mathrm{B}$ in a $1 \mathrm{km}$ race so that the race may end in a dead heat?

In a race of $200 \mathrm{m}, \mathrm{A}$ can beat $\mathrm{B}$ by $35 \mathrm{m}$ and $\mathrm{C}$ by $20 \mathrm{m}.$ In a race of $360 \mathrm{m}, \mathrm{C}$ will beat B by:

$\mathrm{A}$ and $\mathrm{B}$ take part in a $100 \mathrm{m}$ race. A runs at $6 \mathrm{km}/\mathrm{hr}$ and $\mathrm{A}$ gives $\mathrm{B}$ a start of $9 \mathrm{m}$ and still beats him by $18$ seconds. B's speed is:

In $a$ game of $100$ points, $A$ can give $B,20$ points and $C,28$ points. Then, $B$ can give $C:$

At a game of billiards, $A$ can give $B 15$ points in $60$ and $A$ can give $C$ to $20$ points in $60.$ How many points can $B$ give $C$ in a game of $90?$