Introduction / Context:
This question is from the application of volume to real life situations involving water storage and consumption. We are given the capacity of a tank and the daily water requirement of a population. The main steps are to convert the volume of the tank into litres and then divide by the daily consumption to find the number of days for which the supply will last. Such problems are common for practising unit conversions between cubic metres and litres.
Given Data / Assumptions:
- Population of the town = 4000 people.
- Per head daily water requirement = 140 litres.
- Tank dimensions: 18 m by 12 m by 8 m.
- Tank is completely full initially.
- Water usage is uniform and only for this population.
Concept / Approach:
First, compute the volume of the tank in cubic metres. Then convert cubic metres to litres using:
1 cubic metre = 1000 litres
Next, compute the total daily water consumption by multiplying population and per head requirement. Finally, divide the tank capacity in litres by daily consumption to obtain the number of days the water will last.
Step-by-Step Solution:
Step 1: Compute volume of tank in cubic metres.
Volume tank = length * breadth * height
Volume tank = 18 * 12 * 8 cubic metres.
Volume tank = 1728 cubic metres.
Step 2: Convert volume to litres.
Capacity in litres = 1728 * 1000 = 1,728,000 litres.
Step 3: Compute daily water requirement.
Daily requirement per person = 140 litres.
Total daily requirement = 4000 * 140 litres.
Total daily requirement = 560,000 litres.
Step 4: Compute number of days.
Number of days = 1,728,000 / 560,000.
Number of days = 3.0857 approximately.
Considering whole days of full requirement, water will suffice for 3 full days.
Verification / Alternative check:
If we supply water for 3 days, total water consumed = 3 * 560,000 = 1,680,000 litres. Remaining water = 1,728,000 - 1,680,000 = 48,000 litres, which is less than one full day of requirement. Hence three days are possible, but a full fourth day is not. This confirms that the correct answer in whole days is 3.
Why Other Options Are Wrong:
Option B (4 days) would require 4 * 560,000 = 2,240,000 litres, which exceeds the tank capacity. Option C (5 days) and Option E (6 days) are even larger overestimates. Option D (2 days) underestimates the supply duration because two days require only 1,120,000 litres and there will still be enough water left for more than one additional day.
Common Pitfalls:
Students may forget the conversion factor between cubic metres and litres or may miscalculate the total daily requirement by missing a zero. Some also round the days incorrectly or interpret 3.08 as 4 instead of taking only complete days of supply. Always convert units carefully and think about whether the question asks for exact days or whole days.
Final Answer:
The water in the tank will be sufficient for
3 days for the town population.
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