Question

A book shop sold a set of harry potter book series to a book collector for 40 percent more than the store had originally paid for the books. When the collector tried to resell the books to the store, the store bought it back at 50 percent of what the book collector had paid. The shop then sold the book again at a profit of 70 percent on its buy-back price. If the difference between the series of book's original cost to the shop and the book's buy-back price was \$100, for approximately how much did the shop sell the books the second time?

• A. 600
• B. 567
• C. 396
• D. 333
• E. 330

Hint:

In complex percentage problems, it's often easier to work with multipliers. A 40% increase is a multiplier of 1.4, a 50% price is a multiplier of 0.5, and a 70% profit is a multiplier of 1.7. Chaining these multipliers can simplify the setup.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a multi-step percentage problem. We need to track the price of the book series through several transactions to find the final selling price.
Step 2: Detailed Explanation:
Let's define the prices at each stage:

OC (Original Cost): The price the shop initially paid for the books.
SP1 (First Selling Price): The price the collector paid the shop.
BBP (Buy-Back Price): The price the shop paid the collector to buy the books back.
SP2 (Second Selling Price): The price the shop sold the books for the second time.
Let's express each price in terms of the Original Cost (OC):

SP1: The shop sold it for 40% more than OC. \[ SP1 = OC + 0.40 \times OC = 1.4 \times OC \]
BBP: The shop bought it back for 50% of what the collector paid (SP1). \[ BBP = 0.50 \times SP1 = 0.50 \times (1.4 \times OC) = 0.7 \times OC \]
SP2: The shop sold it again for a 70% profit on its buy-back price (BBP). \[ SP2 = BBP + 0.70 \times BBP = 1.7 \times BBP = 1.7 \times (0.7 \times OC) = 1.19 \times OC \]
Now, we use the given information about the difference between the original cost and the buy-back price: \[ OC - BBP = \$100 \] Substitute the expression for BBP in terms of OC: \[ OC - (0.7 \times OC) = 100 \] \[ 0.3 \times OC = 100 \] \[ OC = \frac{100}{0.3} = \frac{1000}{3} \approx \$333.33 \] Finally, we need to find the second selling price (SP2). We already have a formula for it in terms of OC: \[ SP2 = 1.19 \times OC \] Substitute the value we found for OC: \[ SP2 = 1.19 \times \frac{1000}{3} = \frac{1190}{3} \approx 396.67 \] Step 3: Final Answer:
The shop sold the books the second time for approximately \$396.67. The closest answer is 396. This corresponds to option (C).