Answer

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**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.

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