Tickets for an adult cost Rs 1600 and for a child cost Rs 600. Under a special offer, 1 child ticket is given free with every 2 adult tickets. If a group has 17 adults and 7 children, what discount percentage does the group effectively receive on the total ticket cost?

Introduction / Context:

This question combines ticket pricing with a promotional offer that gives free child tickets when a certain number of adult tickets are purchased. You must compare the cost without the offer to the cost with the offer to find the overall discount percentage. Such problems test your ability to handle grouped offers and percentage discount calculations.

Given Data / Assumptions:

• Price of one adult ticket = Rs 1600.
• Price of one child ticket = Rs 600.
• Offer: 1 child ticket free for every 2 adult tickets purchased.
• Group size: 17 adults and 7 children.
• We assume the offer is applied in the most beneficial way for the group.

Concept / Approach:

First, compute the total amount the group would pay if there were no offer at all. Then, apply the offer to determine how many child tickets will be free based on the number of adult tickets. Compute the actual amount paid under the offer. The discount is the difference between the no-offer cost and the offer cost. The discount percentage is calculated relative to the no-offer cost.

Step-by-Step Solution:

Verification / Alternative check:

Compute the fraction 4200 / 31400. Dividing numerator and denominator by 100 gives 42 / 314. This is approximately 0.1337. Multiply by 100 to get 13.37%. This matches the option given and confirms that the discount percentage has been calculated correctly.

Why Other Options Are Wrong:

• 26.02% and 24.41%: These values are much larger and would correspond to a significantly lower payment compared to the original cost, which does not match the calculation.
• 32.2%: This would imply that nearly one third of the total fare is saved, which is inconsistent with only 7 child tickets being free.
• 20%: This is a rough guess and does not match the exact ratio 4200 / 31400.

Common Pitfalls:

Some students miscount the number of free child tickets by taking 17 / 2 as 8.5 and then using 8 or 9 incorrectly. Others may assume only 16 adults count and ignore the extra adult, leading to misapplication of the offer. A further mistake is to compute discount percentage based on the amount paid instead of the original total cost. Always base the percentage discount on the full no-offer amount.

Final Answer:

The group effectively receives a discount of about 13.37%.