A city taxi fare has a fixed charge that covers up to 5 km, plus an additional per-kilometre charge beyond 5 km. The fare for 10 km is ₹350 and for 25 km is ₹800. What is the fare for 30 km?

Introduction / Context:This is a two-parameter linear pricing model: a fixed base fare up to a threshold distance, and a uniform per-kilometre rate beyond that threshold. Two known points (10 km and 25 km) determine the fixed charge and the per-kilometre rate, after which you can predict the fare at 30 km.

Given Data / Assumptions:

• Fixed charge F covers up to 5 km.
• Rate r applies for each km beyond 5 km.
• Fare(10 km) = F + 5r = ₹350.
• Fare(25 km) = F + 20r = ₹800.

Concept / Approach:Solve the two linear equations to find F and r. Then plug into the formula for 30 km: Fare(30) = F + 25r. This is a straightforward system with elimination by subtraction to isolate r.

Step-by-Step Solution:

Verification / Alternative check:Check 25 km: 200 + 20*30 = 200 + 600 = ₹800 (matches). Check 10 km: 200 + 5*30 = ₹350 (matches). Consistency verifies the parameters.

Why Other Options Are Wrong:₹900 assumes a lower rate or base. ₹800 and ₹750 are previous-distance fares. ₹920 is an ad-hoc estimate not supported by the linear model.

Common Pitfalls:Charging per km from 0 instead of after 5 km, or mixing total kilometres with additional kilometres beyond the fixed coverage.

Final Answer:₹ 950