$A$ man travelled a distance of $61 \, km$ in $9 \, h$,partly on foot at the rate of $4 \, km/h$ and partly on bicycle at the rate of $9 \, km/h$. The distance travelled on foot was (in $km$):

$A$ 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 $\text{km/hr}$.

Walking at three-fourth of his usual speed, a man covers a certain distance in $2 \, \text{hours}$ more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is (in $\text{hours}$):

$A$ person started his journey in the morning. At $11:00 \, am$ he covered $\frac{3}{8}$ of the journey and on the same day at $4:30 \, pm$ he covered $\frac{5}{6}$ of the journey. He started his journey at ..... $am$

$A$ $280 \, m$ 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 $m/s$?

$A$ bus started its journey from Bettiah and reached Motihari in $44 \, \text{min}$ with an average speed of $50 \, \text{km/h}$. If the average speed of the bus is increased by $5 \, \text{km/h}$, how much time will it take to cover the same distance? (in $\text{min}$)