Question

If you travel by an autorickshaw the fare for the first kilometre is different from the rate per km for theremaining distance. The total fare for the distance of 20 km is rupees 37.70 and that for a​distance of 26 km rupees 48.50 .Find the auto fare for the first kilometre and for each successive kilometres.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{fare}\mathrm{for}\mathrm{first}\mathrm{kilometre}\mathrm{is}\mathrm{Rs}x\mathrm{and}\mathrm{for}\mathrm{each}\mathrm{successive}\mathrm{kilometre}\mathrm{is}\mathrm{Rs}y. \\ \mathrm{ATQ}, \\ x+19y=37.70.....\left(1\right) \\ x+25y=48.50.....\left(2\right) \\ \mathrm{From}\left(2\right)-\left(1\right),\mathrm{we}\mathrm{get} \\ x+25y-x-19y=48.50-37.70 \\ \Rightarrow 6y=10.80 \\ \Rightarrow y=\frac{10.80}{6}=1.80 \\ \mathrm{Putting}y=1.80\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ x+19\times 1.80=37.70 \\ \Rightarrow x+34.20=37.70 \\ \Rightarrow x=3.50 \\ \mathrm{Hence},\mathrm{fare}\mathrm{for}\mathrm{first}\mathrm{kilometre}\mathrm{is}\mathrm{Rs}3.50\mathrm{and}\mathrm{for}\mathrm{each}\mathrm{successive}\mathrm{kilometre}\mathrm{is}\mathrm{Rs}1.80 \end{gathered}$$