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: To solve this question, we need to know the basic theory related to the chapter surface area and volume. First, we calculate the total Capacity of the tank by multiplying length, breadth and height. And then find the total required per day. And finally, we take the ratio of these two to get the Number of days water lasts.

Complete step-by-step answer:
The dimension of the tank is given as: length = 20m, breadth = 15m and height = 6m.
So, this is a cuboid.
As we know,
Volume of cuboid=length$ \times $ breadth $ \times $height
$ \Rightarrow $ Capacity of tank =l$ \times $b$ \times $h= (20$ \times $15$ \times $6) ${m^3}$
                                             = 1800 ${m^3}$

As we know, $1{\text{ }}{{\text{m}}^3}$=1000 litre. So, we get-
Capacity of tank = 1800000 litre
Therefore, consumption of water in 1 day = 4000$ \times $150 litres
Now,
Number of days water last = $\dfrac{{volume{\text{ of tank}}}}{{total{\text{ }}water{\text{ required per day}}}}$
$ \Rightarrow $ Water of this tank will last for = $\dfrac{{1800000}}{{600000}}$
                                                          = 3 days
Therefore, 3 days will the water of this tank last.


Note:In this question, we need to care about the conversion of units from one dimension to the other dimension. And always remember that Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.