The fare of a bus is $Rs. X$ for the first five kilometres and $Rs. 13$ per kilometer thereafter. If a passenger pays $Rs. 2402$ for a journey of $187$ kilometres,what is the value of $X$? (in $Rs.$)

It takes $8\, hours$ for a $600\, km$ journey,if $120\, km$ is done by train and the rest by car. It takes $20\, minutes$ more,if $200\, km$ is done by train and the rest by car. The ratio of the speed of the train to that of the car is

$A$ train,$240 \, m$ long,crosses a man walking along the line in the opposite direction at the rate of $3 \, km/h$ in $10 \, seconds$. The speed of the train is (in $km/h$):

$A$ man starts running from point $P$ at $11:00$ $a.m.$ with a speed of $10 \, km/hr$. He runs for $2 \, hours$ and then takes a $1 \, hour$ rest. He continues this pattern until he is caught by another man who starts at $2:00 \, p.m.$ from point $P$ and runs non-stop at a speed of $15 \, km/hr$ toward the first man. At what time (in $p.m.$) will the first man be caught?

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:

$A$ passenger train running at the speed of $80 \text{ km/h}$ leaves the railway station $6 \text{ hours}$ after a goods train leaves and overtakes it in $4 \text{ hours}$. What is the speed of the goods train? (in $\text{km/h}$)