An auto rickshaw charges Rs 10 for the first kilometre then Rs 8 for each such subsequent kilometre. The total charge (in Rs) for d kilometres is __________.


Auto rickshaw charges for 1st KM = Rs.10


Charges after 1st KM (i.e., 2nd, 3rd, 4th) = Rs.8


Charges for d KMs = charges for 1st, 2nd, 3rd, 4th, …. d


= charges for 1st + charges for 2nd, 3rd, 4th, …. d-1


( charges for 1 km is separated we write d-1 in the second term instead of d)


= 10 + 8 × (d-1)


We will be charged same amount after 1st that is Rs.8


= 10 + 8d – 8


= 2 + 8d


Total charges for d KMs is 2 + 8d


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