$A$ $280 \, m$ long train moving with an average speed of $108 \, km/h$ crosses a platform in $12 \, seconds$. $A$ boy crosses the same platform in $10 \, seconds$. What is the speed of the boy in $m/s$?

One aeroplane started $30 \, \text{minutes}$ later than the scheduled time from a place $1500 \, \text{km}$ away from its destination. To reach the destination at the scheduled time,the pilot had to increase the speed by $250 \, \text{km/hr}$. What was the original speed of the aeroplane? (in $\text{km/hr}$)

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other,they complete their journeys in $9$ and $16 \, \text{hours}$,respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \, \text{km/h}$?

$A$ man performs $\frac{2}{15}$ of the total journey by rail,$\frac{9}{20}$ by tonga,and the remaining $10 \ km$ on foot. The total journey is (in $km$):

Mohan walks from Tilak Nagar to Moti Nagar and back in a certain time at the rate of $3 \frac{1}{2} \, km/h$. But,if he had walked from Tilak Nagar to Moti Nagar at the rate of $3 \, km/h$ and back from Moti Nagar to Tilak Nagar at the rate of $4 \, km/h$,he would have taken $10 \, minutes$ longer. The distance between Tilak Nagar and Moti Nagar is (in $km$)

$A$ man travelled from the village to the post office at the rate of $25 \, km/hr$ and walked back at the rate of $4 \, km/hr$. If the whole journey took $5 \, hours \, 48 \, minutes$,find the distance of the post office from the village (in $km$).