$A$ certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time,the ratio of the speed of the jogger to that of the cyclist is

Two trains start at the same time from Delhi and Mumbai and move towards each other at the rate of $85 \, km/h$ and $65 \, km/h$ respectively. When they meet,it is found that one train has travelled $20 \, km$ more than the other. Find the distance between Delhi and Mumbai (in $km$).

$A$ man with $\frac{3}{5}$ of his usual speed reaches the destination $2 \frac{1}{2}$ hours late. Find his usual time to reach the destination? (in $hours$)

$A$ train passes a $150 \,m$ long railway bridge in $18 \,seconds$. If the train is running at a speed of $60 \,km/h$,then the length of the train in metres is (in $m$).

$A$ train $100 \, m$ long takes $3 \frac{3}{5} \, s$ to cross a man walking at the rate of $6 \, km/h$ in a direction opposite to that of the train. Find the speed of the train in $km/h$.

$A$ man can reach a certain place in $30 \, \text{hours}$. If he reduces his speed by $\frac{1}{15}^{th}$, he goes $10 \, \text{km}$ less in that same time. Find his speed in $\text{km/hr}$.