Question

20 men can complete their work in \[40\] days. When should \[4\] men leave so that the work may be finished in \[48\] days?

Answer 1

Hint: Firstly, we have to calculate the total number of days, it takes to complete the work by each of the workers. Then we have to calculate the number of days it takes to complete the work if four of the workers leave. Calculating this will give us the required answer.

Complete step by step answer:
Now let us have a brief regarding the linear equation in a single variable. Generally, a linear equation in a single variable forms a straight line upon the graph when plotted. A linear equation is called a linear equation as the degree of the equation is equal to one. The general form of a linear equation is \[ax+b\] where \[a,b\] are real numbers and \[a\] is not equal to zero.
Now let us find when \[4\] men leave so that the work may be finished in \[48\] days.
Firstly, let us find the total number of days required to complete the work.
Number of days required \[=20\times 40=800\]
This is the total number of days required to complete the work, which also means that each worker needs \[800\] days to complete the work.
Now let us calculate when should \[4\] of the workers leave.
Let us consider it as \[x\], which means that after \[x\] number of days \[4\] workers leave the work.
Upon calculating, we get
\[\begin{align}
  & \Rightarrow 20x+16\left( 48-x \right)=800 \\
 & \Rightarrow 20x+768-16x=800 \\
 & \Rightarrow 4x=32 \\
 & \Rightarrow x=8 \\
\end{align}\]
We obtain the value of \[x\] as \[8\].
\[\therefore \] After \[8\] days, four men leave the work so that the work will be completed in \[48\] days.

Note: We must always note the unknown quantity or the value to be calculated with a variable. While solving the linear equations, it would be easier if we transfer the variables to one side of the equation and the constants to the other side of the equation to find the value of the variable.