Sizing a Society Water Tank from Weekly Consumption Data
A housing society has a rectangular overhead tank measuring 2.4 m by 1.8 m by 1.2 m. The outlet stops automatically when 10% of the tank volume remains, so that sediment is not drawn. Daily water consumption for seven days was recorded in litres: 4200, 4500, 3900, 4800, 5100, 4600, 4400. The borewell pump fills the tank at 180 litres per minute, but the society runs it for 25-minute slots. One committee member says, 'The mean is 4,500 litres, so two days need 9,000 litres; the tank is 5,184 litres, so two fills are enough.' Another says, 'The median is also 4,500 litres, so the answer is the same.' The secretary wants a decision that uses the tank's usable capacity, allows a 10% reserve at the end of two days, and considers the highest-consumption day rather than only the average.
1. Calculate the tank's full capacity in litres and its usable capacity after keeping the 10% bottom reserve.
Read the worked answer
Volume = 2.4 × 1.8 × 1.2 = 5.184 m³. Since 1 m³ = 1000 litres, full capacity = 5,184 litres. The outlet stops at 10% remaining, so usable capacity = 0.90 × 5,184 = 4,665.6 litres. The committee's figure of 5,184 litres is the full tank, not the water that can actually be drawn.
2. Find the mean and median daily consumption. Explain why they are equal here and why equality does not make them sufficient for planning.
Read the worked answer
Sum = 4200 + 4500 + 3900 + 4800 + 5100 + 4600 + 4400 = 31,500 litres. Mean = 31,500 ÷ 7 = 4,500 litres. Sorted data: 3900, 4200, 4400, 4500, 4600, 4800, 5100. The median is the 4th value = 4,500 litres. They are equal in this particular data set, but that is a coincidence of the numbers. Both averages hide the peak day of 5,100 litres. A plan based only on 4,500 litres per day can fail on a hot day or when guests arrive, so the highest day and the reserve requirement must also be checked.
3. Using the mean with a 10% end reserve, how many 25-minute pump slots are needed for two days? Then check the highest-consumption day. Is the 'two fills' claim safe?
Read the worked answer
Mean-based two-day need with 10% reserve = 2 × 4500 × 1.10 = 9,900 litres. Each usable fill = 4,665.6 litres. Number of fills = 9,900 ÷ 4,665.6 = 2.122, so round up to 3 fills. Pumping time = 3 × 25 = 75 minutes. Worst-day check: 2 × 5100 × 1.10 = 11,220 litres, which also requires 3 fills because 2 fills give only 2 × 4665.6 = 9,331.2 litres. The 'two fills' claim is unsafe: two usable fills are below even the mean-based requirement of 9,900 litres, and well below the worst-day requirement.