Question

A village having a population of \[4000\], requires \[150\] litres of water per head per day. It has a tank measuring \[20m\times 15m\times 6m\]. For how many days will the water of this tank last?

Answer 1

Hint: Calculate the amount of water consumed by all the people in one day. Also calculate the volume of the tank with given dimensions and convert it into litres by using the conversion formula. To find the number of days the water will last, divide the volume of the tank by the total amount of water consumed by all the people in one day.

Complete step-by-step answer:
We have a village whose population is \[4000\] and each person consumes \[150\] litres of water per day. We have to evaluate the number of days the water in a tank with given dimensions will last.
We will begin by evaluating the volume of the given tank. We know that the volume of a tank whose dimensions are given by \[l,b,h\] is \[lbh\].
Substituting \[l=20,b=15,h=6\] in the above formula, we have the volume of the tank \[=20\times 15\times 6=1800{{m}^{3}}\].
We will now convert this volume of tank into litres. We know that \[1{{m}^{3}}=1000litres\]. Thus, to convert \[x{{m}^{3}}\] into litres, we will multiply \[x\] by \[1000\].
Thus, we have \[1800{{m}^{3}}=1800\times 1000litres=18\times {{10}^{5}}litres\].
So, the volume of a given tank is \[18\times {{10}^{5}}\] litres.
We will now evaluate the amount of water consumed by all the people of the village in one day.
We know that each person consumes \[150\] litres of water in one day and there are \[4000\] people in the village. Thus, to get the total amount of water consumed by all the people, we will multiply the number of people in the village with the amount of water consumed by each person.
Thus, the amount of water consumed by everyone in the village \[=4000\times 150=600000=6\times {{10}^{5}}\] litres.
We will now evaluate the number of days the water will last. To do so, we will divide the total volume of the tank by the amount of water consumed by all the people of the village in one day.
Thus, the number of days water will last \[=\dfrac{18\times {{10}^{5}}}{6\times {{10}^{5}}}=3\].
Hence, with the given details, the water in the tank will last for \[3\] days.

Note: We must be careful about using the units while calculating the volume. Volume of any container is always measured in cubic metres or litres. We also need to be careful about the conversion formula from cubic metres to litres otherwise we will get an incorrect answer.