Question

Form the pair of linear equations for the following problem and find their solution by substitution method:

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10\mathrm{km}$, the charge paid is $\mathrm{Rs}.105$ and for a journey of $15\mathrm{km}$, the charge paid is $\mathrm{Rs}.155$. What are the fixed charges and the charge per km? How much does a person have to pay for traveling a distance of $25\mathrm{km}$?

Answer 1

Step 1: Assume variables and form one equation

Let, the fixed charge (in rupees) $=x$

And, the per kilometer charge (in rupees) $=y$

Now, according to the question,

fixed charge $+$ charge for $10\mathrm{km}=105$

$\Rightarrow$ $x+10\times y=105$

$\Rightarrow$ $x+10y=105$

$\Rightarrow$ $x=105-10y$ …(i)

Step 2: Form the second equation

Again, according to the question,

fixed charge $+$ charge for $15\mathrm{km}=155$

$\Rightarrow$ $x+15\times y=155$

$\Rightarrow$ $x+15y=155$ …(ii)

Step 3: Calculate $y$ by substitution

Substituting the value of $x$ in equation (ii) from equation (i),

$\because$ $x+15y=155$

$\Rightarrow$ $105-10y+15y=155$

$\Rightarrow$ $105+5y=155$

$\Rightarrow$ $5y=155-105$

$\Rightarrow$ $5y=50$

$\Rightarrow$ $y=\frac{50}{5}$

$\Rightarrow$ $y=10$

Step 4: Calculate $x$ by substitution

Substituting the value of $y$ in equation (i),

$\because$ $x=105-10y$

$\Rightarrow$ $x=105-10\times 10$

$\Rightarrow$ $x=105-100$

$\Rightarrow$ $x=5$

Step 5: Calculate the charge for $25\mathrm{km}$

Now, the charge for traveling a distance of $25\mathrm{km}=$ fixed charge $+$ charge for $25\mathrm{km}$

$\Rightarrow$ the charge for traveling a distance of $25\mathrm{km}=x+25\times y$

$\Rightarrow$ the charge for traveling a distance of $25\mathrm{km}=5+25\times 10$ [substituting the values of $x$ and $y$]

$\Rightarrow$ the charge for traveling a distance of $25\mathrm{km}=5+250$

$\Rightarrow$ the charge for traveling a distance of $25\mathrm{km}=255$

Hence, a person has to pay $\mathrm{Rs}.225$ for traveling a distance of $25\mathrm{km}$.