$A$ runs $1 \frac{3}{8}$ times as fast as $B$. If $A$ gives $B$ a start of $120 \, m$ and they reach the goal at the same time,the goal is at a distance of (in $m$)

$A$ and $B$ run a $1 \, km$ race. If $A$ gives $B$ a start of $50 \, m$,$A$ wins by $14 \, sec$. If $A$ gives $B$ a start of $22 \, sec$,$B$ wins by $20 \, m$. The time taken by $A$ to run a $1 \, km$ is (in $sec$):

In a $1000\, m$ race,$A$ beats $B$ by $100\, m$ and $C$ by $200\, m$. By how many meters can $B$ beat $C$ in a race of $1350\, m$?

In a game of $90$ points,$A$ can give $B$ $15$ points and $C$ $30$ points. How many points can $B$ give $C$ in a game of $100$ points?

$A$'s speed is $1 \frac{1}{2}$ times of $B$'s speed. In a race,$A$ gives $B$ a start of $300 \, m$. How long should the race course be so that both reach the winning post simultaneously? (in $m$)

In a race of $600 \, m$,$A$ can beat $B$ by $60 \, m$ and in a race of $500 \, m$,$B$ can beat $C$ by $50 \, m$. By how many meters will $A$ beat $C$ in a race of $400 \, m$?