Tickets for an adult cost Rs 1500 and for a child cost Rs 800. Under an offer, 1 child goes free with every 2 adults. If a group has 25 adults and 12 children, what discount percentage does the group effectively receive on the total ticket cost?

Introduction / Context:

This question again explores a ticket discount scheme where a child ticket is free for every two adult tickets purchased. You must compute the group's overall discount percentage by comparing the cost with and without the offer. It reinforces understanding of grouped offers and effective discount calculations.

Given Data / Assumptions:

• Price of one adult ticket = Rs 1500.
• Price of one child ticket = Rs 800.
• Offer: 1 child free with every 2 adult tickets.
• Group size: 25 adults and 12 children.
• The offer is applied as many times as possible, benefiting the group optimally.

Concept / Approach:

We first compute the total amount the group would pay in the absence of any offer. Then we apply the offer to find how many child tickets are free based on the number of adult tickets. We find the actual amount paid under the scheme and then determine the discount percentage relative to the original total cost.

Step-by-Step Solution:

Verification / Alternative check:

The fraction 9600 / 47100 can be simplified by dividing numerator and denominator by 100 to 96 / 471. Approximating 96 / 471 gives approximately 0.2038. Multiplying by 100 confirms that the discount percentage is about 20.38%. This matches the option listed and verifies our calculation.

Why Other Options Are Wrong:

• 26.47% and 31.60%: These larger discount percentages would correspond to greater reductions in the total payment than what results from 12 free child tickets.
• 25% and 33.33%: These are rounder values but do not reflect the exact ratio of 9600 to 47100, and they do not match the computed effective discount.

Common Pitfalls:

Errors often arise from miscounting how many child tickets can be free. Some may multiply 25 by 1 free child per adult pair and forget to limit by the number of children. Others forget to use the original without-offer total as the base when computing the discount percentage. Carefully track the number of adult pairs, limit free tickets by actual children present, and always calculate discount percentage using the original no-offer cost.

Final Answer:

The group receives an effective discount of about 20.38%.