Question

“A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If he uses 4 people instead of three, how long should they take to complete the job?”

Answer 1

Hint: This question is solved using the Time and Work concept. Time and work problems deal with the simultaneous performance involving the efficiency of an individual or a group and the time taken by them to complete a piece of work.
Whenever some work is done, the total work itself can be taken as one unit.
Inverse Proportion: Two quantities A and B are said to be in inverse proportion if there is an increase in the quantity A, there will be a decrease in the quantity B and vice-versa. In other words, the product of their corresponding values should remain constant. This means that,
$A \times B = k$
where k is a positive number, then the quantities A and B are said to vary inversely.
So, if we increase the number of people on a job, then it will take less time to complete the job.

Complete step-by-step answer:
Let the number of days required by 4 persons to complete the job be x.

Number of days	4	x
Number of persons	3	4

As we increase the number of persons, time taken would decrease.
We can say that,
$\begin{gathered}
  {\text{Persons required (P)}} \propto \dfrac{1}{{{\text{Days to complete the job (D)}}}} \\
   \Rightarrow P \propto \dfrac{1}{D} \\
   \Rightarrow P = \dfrac{k}{D} \\
   \Rightarrow P \times D = k \\
\end{gathered} $
where k is constant of proportionality.
Hence, the number of days and the number of persons required to complete the job are inversely proportional to each other.
$\begin{gathered}
  \therefore {P_1}{D_1} = {P_2}{D_2} \\
  3 \times 4 = 3 \times x \\
  x = \dfrac{{3 \times 4}}{3} \\
  x = 4 \\
\end{gathered} $

∴It would require 4 days to complete the job.

Note: Here, students must note that in these types of questions, first of all, it is very important to find what these quantities are and whether they are inversely proportional or directly proportional. And also remember the value of k that is constant will remain the same, and values of the quantities will change.