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 __________.

Question

Philoid · Accepted Answer

Auto rickshaw charges for 1^st KM = Rs.10

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

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

= charges for 1^st + charges for 2^nd, 3^rd, 4^th, …. 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 1^st that is Rs.8

= 10 + 8d – 8

= 2 + 8d

Total charges for d KMs is 2 + 8d