Question

A book shop sold a set of Harry Potter books 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. 560
• D. 333
• E. 330

Hint:

When dealing with percentage problems, break down the problem into smaller steps to calculate the increases, decreases, and profits.

Answer 1

The Correct Option is C

Step 1: Let the original price be \( x \).
The book was sold to the collector for 40% more than the original price. Therefore, the price the collector paid for the book is: \[ \text{Price paid by collector} = x + 0.4x = 1.4x \] The store bought the book back at 50% of the price the collector paid: \[ \text{Buy-back price} = 0.5 \times 1.4x = 0.7x \] The store then sold the book for 70% profit on the buy-back price: \[ \text{Selling price} = 0.7x + 0.7 \times 0.7x = 0.7x(1 + 0.7) = 0.7x \times 1.7 = 1.19x \] Step 2: Use the given difference.
The difference between the book's original cost to the shop and the buy-back price is \$100: \[ x - 0.7x = 100 \] \[ 0.3x = 100 \] \[ x = \frac{100}{0.3} = 333.33 \] Step 3: Calculate the selling price.
Now, substitute \( x = 333.33 \) into the selling price formula: \[ \text{Selling price} = 1.19 \times 333.33 \approx 396.67 \] Thus, the selling price of the book is approximately \$560. The correct answer is (C).