Q35 of 54 Page 77

The car hire charges in a city comprised of a fixed charge together with the charges for the distance covered. For a journey of 12 km the charges paid are Rs 89 and for a journey of 20 km, the charges are Rs.145. What will a person have to pay for travelling a distance of 30 km?

Let fixed charge be x and charges for the distance covered be y.

Case 1


Distance = 12 km


Total fare = Rs 89


Total fare = Fixed charge + Distance travelled × Charges for the distance


89 = x + 12y


x = 89 – 12y ……(1)


Case 2


Distance = 20 km


Total fare = Rs 145


145 = x + 20y ……(2)


Put value of x from (1) in (2)


145 = 89 – 12y + 20y


145 – 89 = 8y


56 = 8y


y = 56/8


y = 7


Put y = 7 in (1)


x = 89 – (12 × 7)


x = 89 – 84


x = 5


Therefore, a fixed charge is rupees 5 and charge for one km is rupees 7.


Distance = 30 km


Total fare = x + 30y


= 5 + (30 × 7)


= 5 + 210


= 215


Therefore, fare for the distance of 30 km is rupees 215.


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