Question

A field can be irrigated in 20 mins using 6 sprinklers. If two more sprinklers are added for the job, then how much less time will it take to irrigate that field?

Answer 1

Given,
6 sprinklers can irrigate a field in 20 mins.

We know that, if the number of sprinklers will be more, then the time taken to irrigate the field will be less.

$So,\text{Number of sprinklers}\left(x\right)\propto \frac{1}{\text{Time}\left(y\right)}$
$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=6\text{sprinklers}$
$y_1=20\text{mins}$
$x_2=(6+2)=8\text{sprinklers}$
$\text{and,}{y}_2=\text{time taken by 8 sprinklers}$

$\Rightarrow y_2=\frac{x_1\times y_1}{x_2}$
$\Rightarrow y_2=\frac{6\times 20}{8}=15\text{mins}$

So, the difference in time = (20 - 15) = 5 mins.