A person shooting at a target from a distance of $450$ metres finds that the sound of the bullet hitting the target comes $\frac{1}{2}$ seconds after he fired. A person equidistant from the target and shooting point hears the bullet hit $3$ seconds after he heard the gun. The speed of sound is:

A monkey climbs a slippery pole $12 m$ high. It rises $1$ meter in every one minute and slips a half meter in every next minute. Find how soon it will reach the top?

A boy walks at $4 km/hr$ and reaches his school $5$ minutes late. Next day he walks at $5 km/hr$ and start at the same time, reaches his school $10$ minutes early. How far is the school from his house?

A train starts from Delhi with a certain number of passengers. At Ghaziabad, $110$ gets down and $100$ gets in. At Aligrah, $50\%$ gets down and $25$ gets in. At Kanpur, $5$ of them gets down and $50$ gets in. When the train leaves Kanpur, there are $200$ passengers. How many passengers boarded the train at Delhi?

The radius of a circular wheel is $35 cm$ and it moves at the rate of $500$ revolutions per minute. The speed of the wheel is:

Two men $X$ and $Y$, start from a place $P$, walking at $3 km/h$ and $4 km/h$. How much distance apart will they be after $4$ hours if they are walking in the same direction?

Two men $X$ and $Y$, start from a place $P$, walking at $3 km/h$ and $4 km/h$. What will be the distance between them after $5$ hours if they walk in opposite directions?

A person has to make a journey of $72 km$. He rides a cycle at $12 km/h$. After going a certain distance, the cycle got punctured, and he walks the remaining distance at $4\frac{1}{2} km/h$. Where did the cycle get punctured if the total time taken for the journey was $8\frac{1}{2}$ hours?