Two-part linear fare model (fixed + per-km): An auto-rickshaw fare consists of a fixed charge plus a per-kilometer charge. A 10 km trip costs ₹85 and a 15 km trip costs ₹120. What will be the fare for a 25 km trip at the same rates?

Introduction / Context:
Many fare systems combine a base (fixed) fee and a distance-based fee. With two trip-cost data points, we can solve for both unknowns and then predict the cost for any distance under the same pricing scheme.

Given Data / Assumptions:

• Let fixed fee = F and per-km rate = k
• F + 10k = 85
• F + 15k = 120

Concept / Approach:
Subtract the two equations to find k, then back-substitute to find F. Use the linear model to compute the 25 km fare.

Step-by-Step Solution:
(F + 15k) − (F + 10k) = 120 − 85 → 5k = 35 → k = 7F = 85 − 10k = 85 − 70 = 15Fare(25 km) = F + 25k = 15 + 25*7 = ₹190

Verification / Alternative check:
Check the 15 km cost: 15 + 15*7 = 15 + 105 = ₹120 (consistent).

Why Other Options Are Wrong:
₹175, ₹180, ₹200, and ₹225 do not match F + 25k with F = 15 and k = 7.

Common Pitfalls:
Assuming direct proportion from 10 km to 25 km without including the fixed charge, which skews the estimate.

Final Answer:
₹190