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

$A$ $135\, m$ long train is running with a speed of $54\, km/h$. In what time will it pass a telegraph post? (in $seconds$)

$A$ man starts from his home and walks $10 \, km$ towards South. Then he turns right and walks $6 \, km$,again he turns right and goes $10 \, km$. Finally,he turns right and walks $5 \, km$. At what distance is he from his starting point? (in $km$)

$A$ motor car completes a journey in $10 \, hrs$. It covers the first half of the distance at $21 \, km/hr$ and the second half at $24 \, km/hr$. Find the total distance in $km$.

Seeta and Geeta cycled towards each other,one from point $A$ and the other from point $B$,respectively. Seeta left point $A$ $6 \, hours$ later than Geeta left point $B$,and it turned out on their meeting that Seeta had travelled $12 \, km$ less than Geeta. After their meeting,they kept cycling with the same speed,and Seeta arrived at $B$ $8 \, hours$ later and Geeta arrived at $A$ $9 \, hours$ later. Find the speed of the faster cyclist in $km/hr$.

Raj and Prem walk in opposite directions at the rate of $3 \, km/h$ and $2 \, km/h$ respectively. How far will they be from each other after $2 \, hours$? (in $km$)