The owner of a taxi company decides to run all the taxis on CNG fuel instead of petrol/diesel. The taxi charges in the city comprises fixed charges together with the charge for the distance covered. For a journey of 13 km, the charge paid is ₹129 and for a journey of 22 km, the charge paid is ₹210. 

What will a person have to pay for traveling a distance of 32 km? 

Let fixed charge be ₹x and the charge for the distance = ₹y per km 

According to the Question, 

For a journey of 13 km, 

x + 13y = 129 ⇒ x = 129 – 13y —-(i) 

For a journey of 22 km, x + 22y = 210 —(ii) 

⇒ 129 – 13y + 22y = 210 —[From (i)] 

⇒ 9y = 210 – 129 = 81 

⇒ 9y = 81 ⇒ y = 9 

From (i), x = 129 – 13(9) 

= 129 – 117 = 12 

∴ Fixed charge, x = ₹12 

∴ The charge for the distance, y = ₹9 per km 

To pay for traveling a distance of 32 km 

= x + 32y = 12 + 32(9) = 12 + 288 = ₹300