75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m³ of air; find the height of the room.

Given:

Number of persons that can sleep in the room = 75

Air required by each person = 16 m³

Let h be the height of the room.

Dimensions of room = 25 m x 9.6 m x h m

Volume of air in the room = Number of persons x Air required by each person

⇒ 25 x 9.6 x h = 75 x 16

⇒ 240 x h = 75 x 16

⇒ 240 x h = 1,200

⇒ h = $\dfrac{1,200}{240}$

⇒ h = 5 m

Hence, the height of the room is 5 m.