Question

Form the pair of linear equation for the following problems and find their solution by substituting method .
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered . For distance of $10$ the charge paid is Rs $105$ and for a journey of $15$ km the charge paid is Rs $155$ . What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of a $25$ km ?

Answer 1

Let the fixed charge for taxi $=Rsx$

And the variable cost per km $=Rsy$

Total cost =fixed charge +variable charge

Given that for a distance of $10km$ the charge paid is $Rs105$

$x+10y=105$

$x=105-10y...\left(i\right)$

Given that for journey of $15km$ the charge paid is $Rs155$

$x+15y=155$

Put the value of x we get

$105-10y+15y=155$

$5y=155-105$

$5y=50$

$y=10$

put $y=10$ in eq (i)

$x=105-10\left(10\right)=105-100=5$

People have pay for travelling a distance of 25km

$=x+25y$

$=5+25\left(10\right)=5+250=255$

Apeaple have to pay Rs 255 for 25 km