Water flows into a tank measuring 200 m × 150 m through a rectangular pipe of…

Concept: The volume of water needed to raise the level in a cuboidal tank equals its length × breadth × the height by which the level rises (Volume of a cuboid = Length × Breadth × Height). Water flowing through a rectangular pipe delivers a volume every minute equal to the pipe's cross-sectional area multiplied by how far the water column moves in that minute (its speed, converted to metres per minute). The time required is then the total volume needed divided by this flow rate per minute.

Application:

1. Volume of water required for the tank's level to rise by 2 m: 200 m × 150 m × 2 m = 60,000 m3 (using Volume = Length × Breadth × Height).

2. Convert the pipe's flow speed from km/h to m/min: 20 km/h = (20 × 1000) ÷ 60 m/min = 1000/3 m/min, approximately 333.33 m/min.

3. Cross-sectional area of the rectangular pipe: 1.5 m × 1.25 m = 1.875 m2.

4. Volume of water flowing in per minute = area × speed = 1.875 × 1000/3 = 625 m3 per minute.

5. Required time = Total volume ÷ Flow rate per minute = 60,000 ÷ 625 = 96 minutes.

Cross-check: 625 m3/min × 96 min = 60,000 m3, exactly the volume the tank needs to rise by 2 m — confirming the result independently.

Hence, the water level will rise by 2 metres in 96 minutes.