Question

In a school, on a clean village day 150 students take 6 hours to clean a village, if 180 students do this work, then find the time taken to clean the village completely in hours?

Answer 1

Hint: First analyze that the given relation is in direct proportion of inverse proportion, then use the relation of proportion to find the value of the proportionality constant. Then use that value to find the required time needed to clean the village by 180 students.

Complete step-by-step answer:
We have given 150 students take 6 hours to clean the village on the clean village day.
The goal is to find the time taken by the 180 students to clean the village completely.
It can be noticed, as the number of students decreases then the time taken to clean the village increases and as the number of students increases then the time taken to clean the village decreases.
Therefore, the given relation is in inverse proportion, so we have
Number of students$ \propto \dfrac{1}{{{\text{Time taken}}}}$
The Number of students$ = \dfrac{k}{{{\text{Time taken}}}}$, here $k$ is the constant of proportionality.
Then, for the first case, 150 students take 6 hours to clean village so substitute the values into the equation:
$150 = \dfrac{k}{6}$
Solve the equation for the value of $k$:
$k = 150 \times 6$
$ \Rightarrow k = 900$
Now, for the second case, there are 180 students, so we have
$180 = \dfrac{k}{{{\text{Time taken}}}}$
Substitute the value $k = 900$ into the equation:
$180 = \dfrac{{900}}{{{\text{Time taken}}}}$
${\text{Time taken}} = \dfrac{{900}}{{180}}$
${\text{Time taken}} = 5$
Therefore, when 180 students clean the village then the village is completely cleaned in $5$ hours.

Note:It can be noticed that when the number of students increases then it will take less to finish the work and when the number of students decreases then it will take more time to finish the work, such a relation is defined as the inverse relation of proportionality.