Answer :

Total distance covered = x km


Total fare = Rs y


Charges for 1 km = Rs 20


Charges for 2 kms = Rs 20 + Rs 12


Charges for 3 kms = Rs 20 + Rs 12 × 2


Continuing, we get,


Charges for (x – 1) kms = Rs 20 + Rs 12 × (x – 2)


Charges for x kms = Rs 20 + Rs 12 × (x – 1)


Total fare = Rs y


Therefore,


Total fare = Charges for x kms


y = 20 + 12 × (x – 1)


y = 20 + 12x – 12


y = 12x + 8


Let x = 1 then, y = 12x + 8


y = 12× 1 + 8


y = 12 + 8


y = 20


Let x = 5 then, y = 12x + 8


y = 12× 5 + 8


y = 60 + 8


y = 68


Let x = 10 then, y = 12x + 8


y = 12× 10 + 8


y = 120 + 8


y = 128


Plotting, (1, 20), (5, 68) and (10, 128) on the graph we get,


The blue line indicates the required graph of y = 12x + 8



When x = 16, we take 16 on x axis.


Draw a line from 16 on x axis which is parallel to y axis and meets the blue line.


Clearly from the graph the value at y axis is 200


Therefore, taxi charges at covering 16 km = Rs 200


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