Question

A water tank is filled in 15 hours by water falling from 4 pipes of same diameter. What will be time taken to fill the same water tank when only 3 such pipes are opened at the beginning when the tank is empty

Answer 1

Solution!!

Given that 4 pipes of same diameter fill a tank in 15 hours. So, let's first calculate the time taken by 1 pipe to fill the tank.

4 pipes = 15 hours

1 pipe = 15 × 4 hours

1 pipe = 60 hours

So, it takes 60 hours for 1 pipe to fill the tank. We have to calculate the amount of time taken by 3 such pipes to fill the tank.

1 pipe = 60 hours

3 pipes = 60 ÷ 3 hours

3 pipes = 20 hours

It will take 20 hours for 3 pipes to fill the entire tank.

Answer 2

$\large\underline{\sf{Solution-}}$

Given that, A water tank is filled in 15 hours by water falling from 4 pipes of same diameter.

Now, we have to find, what time will be taken to fill the same water tank when only 3 such pipes are opened at the beginning when the tank is empty.

Now, as less number of pipes are there, more time is taken to fill the tank. It means, Number of pipes and time taken are in inverse Variation.

So,

$\begin{array}{|c|c|c|c} \hline \rm Number \: of \: pipes&\rm 4&\rm x \\ \hline\rm Time \: taken \: (in \: hrs)&\rm 15&\rm 3 \\ \hline \end{array}$

Now, using the Law of inverse Variation, we have

$\rm \: 4 \times 15 = 3 \times x$

$\rm \: 60 = 3x$

$\rm\implies \:x = 20 \: hrs$

Hence,

Time taken to fill the same water tank when only 3 such pipes are opened at the beginning when the tank is empty is 20 hours.

$\rule{190pt}{2pt}$

Basic Concept Used :-

Inverse Variation :- Two variables x and y are said to be in inverse or indirect Variation, if there is increase in x, then there is decrease in y or if there is decrease in x, then there is increase in y.