Adult–child fare ratio application An adult fare is six times a child fare. If one adult fare is ₹ 114, what is the total for 4 adults and 5 children traveling the same distance?

Introduction / Context:
Ratio-based unit pricing questions require converting one known fare into the other using the given multiple, then totaling for a group mix. It checks comfort with proportional reasoning and simple arithmetic.

Given Data / Assumptions:

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

Concept / Approach:
First determine the child fare from the adult fare using the 6:1 relation. Then compute the sum for the exact group composition by multiplying fares by counts and adding results.

Step-by-Step Solution:
Given A = ₹ 114 and A = 6C ⇒ C = 114 / 6 = ₹ 19.Cost for 4 adults = 4 * 114 = ₹ 456.Cost for 5 children = 5 * 19 = ₹ 95.Total = 456 + 95 = ₹ 551.

Verification / Alternative check:
Check the ratio: 114 is indeed 6 times 19. The totals are simple whole-number multiplications, so the sum is reliable.

Why Other Options Are Wrong:
₹ 505, ₹ 560, ₹ 572: These correspond to incorrect child fare calculations or arithmetic mistakes in the group totals.

Common Pitfalls:
Taking 114/5 instead of 114/6 for the child fare or miscounting children/adults. Reconfirm the multiple (adult is six times child) before computing.

Final Answer:
₹ 551