Question

Question 3 (iv)
Form the pair of linear equations for the following problems and find their solution by substitution method:
The taxi charges in a city consisting of a fixed charge together with the charge for the distance covered. For a distance of 10 km, 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 25 km?

Answer 1

Let the fixed charge for taxi = Rs x
And variable cost per km = Rs y
Total cost = fixed charge + variable charge
Given that for a distance of 10 km, the charge paid is Rs 105.
x + 10y = 105 … (i)
$\Rightarrow$ x = 105 - 10y
Given that for a journey of 15 km, the charge paid is Rs 155.
x + 15y = 155 … (ii)
Substituting the value of x in equation (ii), we get,
105 - 10y + 15y = 155
$\Rightarrow$ 5y = 155 - 105
$\Rightarrow$ 5y = 50
Dividing by 5, we get
$y=\frac{50}{5}=10$
Substituting this value in equation (i) we get,
x = 105 - 10 $\times$ 10
x = 5
People have to pay for traveling a distance of 25 km.
= x + 25y
= 5 + 25 $\times$ 10
= 5 + 250
= 255
A person has to pay Rs 255 for 25 km.