Question

A plumber can be paid under two schemes as given below:-
Scheme I:- \[Rs.500\] and \[Rs.70\]per hour.
Scheme II:- \[Rs.120\] per hour
If the job takes \[x\] hours for how many values of \[x\] does the scheme give the plumber the better wages?

Answer 1

Hint: We can solve this problem using basic time and work. First we will form equations for both the schemes with \[x\] hours. After that we want to find better wages for scheme I. For this we will write an inequality and simplify it to find the value of x.

Complete step-by-step answer:
Given in the question
It takes \[x\] hours
So we will calculate the wages for both the schemes.
For scheme I it is given that Rs.500 and Rs.70 per hour.
So we will write the equation that depicts the scheme.
We know the hours are \[x\] then the equation will look like
\[\Rightarrow 500+70\times x\]
Now we have to write the equation for scheme II
For scheme II it is given that Rs.120 per hour.
So we will write the equation with the \[x\] hours will look like
\[\Rightarrow 120\times x\]
Now we want that scheme I is better.
So to make scheme I better we write the inequality as
\[\Rightarrow 500+70\times x>120\times x\]
By simplifying it we will get
\[\Rightarrow 500+70x>120x\]
\[\Rightarrow 500>120x-70x\]
We will get
\[\Rightarrow 500>50x\]
Now to simplify it we have to divide the inequality with 50 on both sides of the equation.
\[\Rightarrow \dfrac{500}{50}>\dfrac{50x}{50}\]
We will get
\[\Rightarrow 10>x\]
By rewriting it we will get
\[\Rightarrow x<10\]
From this we can write to get better wages for scheme I we have to get the values between 1 to 9.

Note: We can check the answer by substituting the x value in the above two equations. We will get greater value for scheme I then we can verify our solution. We have to write the inequality according to the question given.