Question

Arun, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai consist of a fixed charge together with the charges for the distance covered. His office is at a distance of 10 km from his home. For a distance of 10 km to his office, Arun paid ₹105. While coming back home, he took another route. He covered a distance of 15 km and paid ₹155.

Based on the above information, answer the following questions.

(i) What are the fixed charges?

(ii) What are the charges per kilometre?

(iii) If fixed charge are ₹20 and charges per kilometre are ₹10 then how much would Arun have to pay for travelling a distance of 10 km?

(iv) Find the total amount paid by Arun for travelling 10 km from home to office and 25 km from office to home. [Fixed charges and charges per kilometre are as in (i) and (ii).]

Answer 1

Let the fixed charge be ₹x and the charge per km be ₹y.

Equations from the given data: \[x + 10y = 105\] \[x + 15y = 155\] 

Subtracting the first from the second: \[5y = 50 \Rightarrow y = 10\] 

Substituting in the first: \[x = 105 - 100 = 5\] 

(i) Fixed charge = ₹5.

(ii) Charge per km = ₹10.

(iii) Amount for 10 km with fixed charge ₹20: \[20 + 10 \times 10 = ₹120\] 

(iv) Home to office (10 km): \[5 + 10 \times 10 = ₹105\] 

Office to home (25 km): \[5 + 25 \times 10 = ₹255\] 

Total amount: \[105 + 255 = ₹360\]