Mathematics
An auto-rikshaw fare starts at ₹25 and remains the same for the initial 2 km. Then it increases by ₹15 per km. For how many km will the fare be ₹130?
Polynomials
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Answer
Let x be the total distance travelled (in km) and F be the fare (in ₹).
For the initial 2 km, the fare is ₹25. After 2 km, the fare increases by ₹15 for every additional km. So for x km (where x ≥ 2), the fare is:
F = 25 + 15(x − 2)
Given that the fare is ₹130, we have:
130 = 25 + 15(x − 2)
⇒ 15(x − 2) = 130 − 25
⇒ 15(x − 2) = 105
⇒ x − 2 =
⇒ x − 2 = 7
⇒ x = 7 + 2
⇒ x = 9
Hence, the fare will be ₹130 for a travel of 9 km.
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