A city taxi fare consists of a fixed charge plus a per-kilometre rate. If 16 km cost Rs 156 and 24 km cost Rs 204, what will be the fare for 30 km?

Introduction / Context:
This linear model problem involves finding a fixed fee and a variable per-kilometre rate using two data points. Such fare questions model cost = fixed component + (rate * distance).

Given Data / Assumptions:

• Total fare for 16 km = Rs 156.
• Total fare for 24 km = Rs 204.
• Fare = F + r * d, where F is fixed charge and r is Rs/km.

Concept / Approach:
Set up two linear equations in F and r using the two trips. Solve simultaneously, then compute the fare for 30 km by substitution.

Step-by-Step Solution:
Equation 1: F + r * 16 = 156.Equation 2: F + r * 24 = 204.Subtract Eq1 from Eq2: (F cancels) → r * (24 − 16) = 204 − 156 → 8r = 48 → r = 6 Rs/km.Back-substitute into Eq1: F + 6 * 16 = 156 → F + 96 = 156 → F = 60.Fare for 30 km: F + r * 30 = 60 + 6 * 30 = 60 + 180 = Rs 240.

Verification / Alternative check:
Check with 24 km: 60 + 6 * 24 = 60 + 144 = 204 (matches data). Model is consistent.

Why Other Options Are Wrong:

• Rs. 236, Rs. 248, Rs. 252, Rs. 258: Do not satisfy the linear model with F = 60 and r = 6.

Common Pitfalls:

• Mistaking the difference in costs per extra km (48 over 8 km) as the fixed part.
• Arithmetic slips in subtraction or multiplication.

Final Answer:
Rs. 240