$A$ 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 $km$)

$A$ man covers a certain distance between his house and office on a scooter. With an average speed of $30 \, km/hr$,he is late by $10 \, min$. However,with a speed of $40 \, km/hr$,he reaches his office $5 \, min$ earlier. Find the distance between his house and office in $km$.

$P$ and $Q$ are $27 \, km$ apart. Two trains with speeds of $24 \, km/h$ and $18 \, km/h$ respectively start simultaneously from $P$ and $Q$ and travel in the same direction. They meet at a point $R$ beyond $Q$. The distance $QR$ is (in $km$):

$A$ train travelling with a speed of $60 \, km/h$ catches another train travelling in the same direction and then leaves it $120 \, m$ behind in $18 \, seconds$. The speed of the second train is (in $km/h$):

Two boys jointly begin to write a booklet containing $817$ lines. The first boy starts with the first line and writes $200$ lines an hour. The second boy starts with the last line,then writes line $816$ and so on,proceeding backwards at the rate of $150$ lines an hour. They will meet on:

Two trains,Kanpur Mail and Delhi Mail,start at the same time from stations Kanpur and Delhi respectively towards each other. After passing each other,they take $12\, \text{hours}$ and $3\, \text{hours}$ to reach Delhi and Kanpur respectively. If the Kanpur Mail is moving at the speed of $48\, \text{km/hr}$,the speed of the Delhi Mail is (in $\text{km/hr}$):