Adult fare is six times child fare: Between Rajpur and Mirpur, one adult ticket costs ₹114, which is six times a child ticket. What is the total fare for 4 adults and 5 children together for the same trip?

Introduction / Context:
Typical fare-ratio problems use a direct proportional relation between adult and child fares. Given the adult price, we find the child price, and then scale to the specified group counts to compute the total bill.

Given Data / Assumptions:

• Adult fare A = ₹114.
• A = 6 * child fare (C) ⇒ C = A/6.
• Group: 4 adults and 5 children.

Concept / Approach:
Compute the unit child fare, then sum 4*A + 5*C. This is a single-step arithmetic calculation once C is identified from the ratio.

Step-by-Step Solution:

Verification / Alternative check:
Check dimensions: rupees across, and integer arithmetic throughout. No rounding is needed as values are exact.

Why Other Options Are Wrong:

• ₹505/-, ₹545/-, ₹560/-, ₹572/-: Do not match the exact linear sum 456 + 95.

Common Pitfalls:
Using 5 children * ₹18 (rounding) or misreading “six times” as “six more.” “Six times” means a multiplier, not an additive increase.

Final Answer:
₹ 551/-