Problem Statement:
A pump on the ground floor of a building can pump up water to fill a tank of volume 30m3 in 15 min. If the tank is 40m above the ground and the efficiency of the pump is 30%, we need to determine the amount of electric power consumed by the pump.

Solution:

Step 1: Calculate the amount of work done by the pump:
Given that the volume of the tank is 30m3, we can convert it to liters by multiplying by 1000:
Volume of the tank = 30m3 = 30,000 liters

The work done by the pump is equal to the weight of the water lifted to the tank. The weight of water can be calculated using the formula:
Weight = Volume × Density × Gravity

The density of water is approximately 1000 kg/m3, and the acceleration due to gravity is 9.8 m/s2.
Weight of water = 30,000 liters × 1000 kg/m3 × 9.8 m/s2

Step 2: Calculate the height the pump lifts the water:
Given that the tank is 40m above the ground, the height the pump lifts the water is 40m.

Step 3: Calculate the work done against gravity:
The work done against gravity can be calculated using the formula:
Work = Force × Distance

Force = Weight of water = 30,000 liters × 1000 kg/m3 × 9.8 m/s2
Distance = Height = 40m

Work done against gravity = (30,000 liters × 1000 kg/m3 × 9.8 m/s2) × 40m

Step 4: Calculate the total work done:
The total work done by the pump is the sum of the work done against gravity and the work done against friction or other losses.

Total work done = Work done against gravity + Work done against friction or other losses

Step 5: Calculate the electric power consumed:
The electric power consumed by the pump can be calculated using the formula:
Power = Work done / Time

Given that the pump fills the tank in 15 min, we need to convert it to seconds:
Time = 15 min × 60 sec/min

Electric power consumed = Total work done / Time

Step 6: Calculate the efficiency of the pump:
The efficiency of the pump is given as 30%, which can be converted to a decimal form:
Efficiency = 30% = 0.30

Step 7: Calculate the electric power input:
The electric power input to the pump can be calculated using the formula:
Electric power input = Electric power consumed / Efficiency

Finally, we can substitute the values into the equations and calculate the electric power input consumed by the pump.