The taxi charges in a city consist of a fixed charge together with the charge for the distance covered.

Question

Form the pair of linear equations for the following problems 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 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 of the taxi be Rs. x. 

If the charge for each km is Rs. y, then 

Fixed charge + Charge for 10 km = Rs. 105 

∴ x + 10y = 105 ………. (i) 

Fixed charge + Charge for 15 km travelled 

= Rs. 155 

∴ x + 15y = 155 ……….. (ii) 

From eqn. (i), 

x + 10 y = 105 

x = 105 – 10y 

Substituting the value of ’x’ in eqn. (ii), 

x + 15y = 155 

105 – 10y + 15y = 155 

105 + 5y = 155 

5y = 155 – 105 

5y = 50

∴ y = \(\frac{50}{5}\)

∴ Rs. y = 10.

Substituting the value of y in 

x = 105 – 10y, 

= 105 – 10 × 10 

= 105 – 100 

∴ x = Rs. 5 

∴ Fixed Charge of Taxi is Rs. 5. 

Charge for each km is Rs. 10 

Charge for 1 km is Rs. 10 

Charge for 25 km ? 

∴ 25 × 10 = Rs. 250.