Question

A plumber can be paid under two schemes as given below:

$$\begin{gathered} \mathrm{I}:\mathrm{Rs}.600\mathrm{and}\mathrm{Rs}.50\mathrm{per}\mathrm{hour}. \\ \mathrm{II}:\mathrm{Rs}.170\mathrm{per}\mathrm{hour}. \end{gathered}$$
If the job takes $n$ hours, for how many values of $n$ does the Scheme I give the plumber the better wages?

Answer 1

Step 1:

Determine the equations:

The total number of hours a job takes is $n\mathrm{hours}.$

Therefore, the wage earned according to scheme I$=600+\left(50\times n\right)$

The wage earned according to scheme II$=170\times n$

Step 2:

Find the values of $n$:

For scheme I to be better for wages:

$\begin{array}{rcl}\mathrm{Wages}\mathrm{earned}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{scheme}\mathrm{I}& >& \mathrm{Wages}\mathrm{earned}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{scheme}\mathrm{II}\\ & \Rightarrow & 600+\left(50\times n\right)>170\times n\\ & \Rightarrow & 600+50n>170n\\ & \Rightarrow & 600>170n-50n\left[\mathrm{Subtracting}50n\mathrm{on}\mathrm{both}\mathrm{sides}\right]\\ & \Rightarrow & 600>120n\\ & \Rightarrow & \frac{600}{120}>n\left[\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}120\right]\\ & \Rightarrow & 5>n\\ \therefore n& <& 5\end{array}$

Therefore, for $n<5$ hours, scheme I gives the plumber better wages.