The ticket price for an adult is Rs. 1600 and for a child is Rs. 1200. One child goes free with every two adults. If a group has 23 adults and 10 children, what is the discount percentage received by the group?

Introduction / Context:
This question is based on a promotional offer scenario and tests percentage discount calculation. The key is to correctly understand how many child tickets become free under the given condition, then compare the amount saved with the original total ticket cost.

Given Data / Assumptions:

• Adult ticket price = Rs. 1600.
• Child ticket price = Rs. 1200.
• Offer: one child ticket is free with every two adults.
• The group has 23 adults and 10 children.
• We must find the overall discount percentage for the group.

Concept / Approach:
First compute the total amount that would be paid without any offer. Next, apply the offer: for every pair of two adults, one child ticket becomes free, limited by the actual number of children. Then calculate the actual amount paid and use the formula discount percentage = (savings / original amount) * 100.

Step-by-Step Solution:
Original total without offer = 23 * 1600 + 10 * 1200.This equals 36800 + 12000 = Rs. 48800.Number of adult pairs = floor(23 / 2) = 11 pairs, but there are only 10 children.So all 10 children can travel free under the offer.Actual amount paid = payment for 23 adults only = 23 * 1600 = Rs. 36800.Savings = 48800 - 36800 = Rs. 12000.Discount percentage = (12000 / 48800) * 100 ≈ 24.59 percent.

Verification / Alternative check:
We can check by treating the free tickets as a direct discount on the original bill. Ten child tickets at Rs. 1200 would cost Rs. 12000. The discount percentage is simply 12000 divided by the original total 48800, leading again to approximately 24.59 percent.

Why Other Options Are Wrong:
Percentages like 25.95, 25.77 and 31.60 come from using wrong original totals, incorrect numbers of free children or mathematical errors in computing the ratio. Only 24.59 percent is consistent with the exact savings and original bill amount.

Common Pitfalls:
Some students assume that only full sets of two adults and one child count and mis-handle the leftover adults. Others apply the discount on adult tickets as well, which the offer does not allow. Always translate the offer wording into precise arithmetic steps.

Final Answer:
The group receives an overall discount of approximately 24.59 percent.