Tickets for an adult cost Rs. 2200 and tickets for a child cost Rs. 990.\nOne child can travel free with every two paying adults.\nIf a group consists of 23 adults and 11 children, what is the overall discount percentage that the group receives compared to paying full fare for everyone?

Introduction / Context:
This problem tests percentage discount concepts in the context of a group ticket offer. Instead of a standard percentage discount on price, the offer is framed as free tickets for children under certain conditions. To find the effective discount, we must compare what the group would have paid without the offer to what they actually pay with the offer. This is a realistic commercial arithmetic scenario.

Given Data / Assumptions:

• Adult ticket price = Rs. 2200 each.
• Child ticket price = Rs. 990 each.
• Offer: One child goes free for every two paying adults.
• Group composition: 23 adults and 11 children.
• The offer is applied as many times as possible using the ratio of 2 adults to 1 free child.

Concept / Approach:
First, we calculate the total amount the group would pay without any offer. Next, we apply the offer: for every pair of two adults, one child ticket becomes free, up to the number of children available. Then we compute the total amount actually paid under the offer. The effective discount percentage is then (no offer cost - offer cost) / no offer cost * 100. The important part is to match each free child only with complete pairs of adults.

Step-by-Step Solution:
Step 1: Total cost with no offer: adults cost = 23 * 2200, children cost = 11 * 990.Step 2: Compute adult cost: 23 * 2200 = 50,600 rupees.Step 3: Compute child cost: 11 * 990 = 10,890 rupees.Step 4: Total cost without offer = 50,600 + 10,890 = 61,490 rupees.Step 5: Apply the offer: one free child per two paying adults. With 23 adults, there are 11 full pairs of adults and 1 adult left over.Step 6: The group has 11 children, so all 11 children can go free, because there are 11 pairs of adults.Step 7: Under the offer, the group pays for 23 adult tickets and 0 child tickets.Step 8: Total cost with offer = 23 * 2200 = 50,600 rupees.Step 9: Discount amount = 61,490 - 50,600 = 10,890 rupees.Step 10: Effective discount percentage = (10,890 / 61,490) * 100 ≈ 17.71 percent.

Verification / Alternative check:
Notice that the discount amount equals the total cost of all 11 children when there is no offer. This is because each child is free under the scheme. So the discount amount should be 11 * 990 = 10,890 rupees, which matches the difference we computed. Dividing this discount by the no offer cost 61,490 gives the effective discount proportion, which evaluates to approximately 0.1771, or 17.71 percent. This confirms the calculation.

Why Other Options Are Wrong:
32.30 percent and 26.47 percent would both require a much larger discount amount than the total cost of all children, which is impossible under this scheme.
25.77 percent is close sounding but still significantly larger than the correct discount fraction and does not match the exact calculation.
10 percent represents a much smaller saving than the free travel of 11 children and is therefore clearly incorrect.

Common Pitfalls:
One common error is to assume that the offer gives a flat percentage discount on all tickets, instead of carefully counting how many children actually get free travel. Another mistake is incorrectly grouping adults and children, for example, assigning more than one free child per pair of adults or forgetting to cap the free children by the actual number of children in the group. Always compute the full price first, then accurately model the offer, and finally compare the two totals to get the effective discount percentage.

Final Answer:
The group receives an effective discount of approximately 17.71 percent.