Question
Restaurants A, B, C, and D give the following offers:
A: one mocktail free for every two purchased
B: one mocktail free for every three purchased
C: two mocktails free for every six purchased
D: 30% discount on each mocktail
If all of the restaurants have the same marked price for each mocktail, in which restaurant would you pay the least if you drank eight mocktails?
The correct answer is
D
The question asks to determine which restaurant offers the lowest price for eight mocktails, given the same marked price ($P$) for each mocktail and different offers.
Restaurant Offer Analysis
Let $P$ be the marked price of one mocktail.
- Restaurant A: 1 mocktail free for every 2 purchased. This implies paying for 2 mocktails grants 3 mocktails.
- Restaurant B: 1 mocktail free for every 3 purchased. This implies paying for 3 mocktails grants 4 mocktails.
- Restaurant C: 2 mocktails free for every 6 purchased. This implies paying for 6 mocktails grants 8 mocktails.
- Restaurant D: 30% discount on each mocktail.
Cost Calculation for 8 Mocktails
We calculate the total cost for 8 mocktails at each restaurant:
- Restaurant A: To receive 8 mocktails, you pay for $8 \times \frac{2}{3}$ mocktails. Since you must purchase whole mocktails, you need to purchase $\lceil \frac{16}{3} \rceil = 6$ mocktails. The total cost is $6P$.
- Restaurant B: To receive 8 mocktails, you pay for $8 \times \frac{3}{4} = 6$ mocktails. The total cost is $6P$.
- Restaurant C: The offer directly provides 8 mocktails (6 purchased + 2 free). You pay for 6 mocktails. The total cost is $6P$.
- Restaurant D: The price per mocktail is $P \times (1 - 0.30) = 0.70P$. For 8 mocktails, the total cost is $8 \times 0.70P = 5.6P$.
Cost Comparison and Conclusion
Comparing the total costs for 8 mocktails:
- Restaurant A: $6P$
- Restaurant B: $6P$
- Restaurant C: $6P$
- Restaurant D: $5.6P$
The lowest cost is $5.6P$, which occurs at Restaurant D.
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Important Questions from Profit & Loss (Notes)
- A person incurs a loss of 10% by selling a watch for Rs. 450. At what price should the watch be sold to earn 10% profit?
- A shopkeeper bought an item for ₹7825 and marked it at 30% higher than the cost price. If he sells the item by allowing 20% discount, then his profit percentage will be :
- A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?
- A dealer buys two articles X and Y for ₹500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns ₹958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?
- A shopkeeper earned a profit (in ₹) by selling an item, which is three times the discount offered (in ₹). If the discount offered is 6.25%, what is his profit percentage ?
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