Water flows through a rectangular pipe of cross-section 1.5 m × 1.25 m at a speed of 20 km/h into a rectangular tank 100 m × 150 m. In how much time will the water level in the tank rise by 2 m?

Introduction / Context:We find the time needed to raise a tank’s water level by a fixed height using inflow rate from a pipe. The inflow is area × velocity; the needed volume is tank base area × rise in height.

Given Data / Assumptions:

• Pipe cross-section: 1.5 m × 1.25 m ⇒ A = 1.875 m^2.
• Flow speed: 20 km/h = 20000 m / 3600 s ≈ 5.5556 m/s.
• Tank: 100 m × 150 m; rise needed = 2 m ⇒ volume needed = 100*150*2.

Concept / Approach:

• Flow rate Q = A * v (m^3/s).
• Required volume V = base area * height rise.
• Time t = V / Q.

Step-by-Step Solution:

Verification / Alternative check:Using fractional speed v = 50/9 m/s → Q = 1.875*(50/9) = 93.75/9 = 10.4167, same result; t unchanged.

Why Other Options Are Wrong:

• 96, 75, 50 min: Do not satisfy V = Q*t with the given dimensions and speed.
• None of these: Incorrect; 48 min matches the exact computation.

Common Pitfalls:

• Forgetting to convert km/h to m/s.
• Using perimeter instead of area for the pipe section.
• Miscalculating the tank volume rise.

Final Answer:48 min