2470.52 – Teapot Trade

Katie imports brown English teapots for a local Curiosity Shop. They cost her a certain amount cc, and her profit, when she sells them in the shop, is x%x\% of this amount. Her mother has just found a new and cheaper source of teapots. They will now cost Katie 88 percent less. Does she lower her price in the shop? Never! She maintains the same price and her profit now turns out to be (x+10)(x + 10) percent. What was her original profit xx?

. (Thanks, Mom)

  1. 12%12\%

  2. 15%15\%

  3. 30%30\%

  4. 50%50\%

  5. 75%75\%

Solution

If cc is the original cost to Katie, then (x100)⋅c\left(\dfrac{x}{100}\right) \cdot c is her profit, which is also what Curiosity Shop must mark-up Katie's price in order that she obtain this profit. Thus the selling price in the Curiosity Shop is

Price = Cost + Markup=c+xc100=100c+xc100.\text{Price } = \text{ Cost } + \text{ Markup} = c + \dfrac{xc}{100} = \dfrac{100c + xc}{100}.

The new cost to Katie is 0.92c0.92 c, and her new profit is (x+10)/100⋅(0.92c)(x + 10)/100 \cdot (0.92c). The new selling price is

New Price = Cost + Markup=0.92c+(x+10)(0.92c)100=92c+(x+10)(.92c)100.\text{New Price } = \text{ Cost } + \text{ Markup} = 0.92 c + \dfrac{(x + 10)(0.92c)}{100} = \dfrac{92c + (x + 10)(.92c)}{100}.

But the new and old prices are the same. So,

100c+xc=92c+(x+10)(.92c)100c + xc = 92c + (x + 10)(.92c)

or

8c+xc=.92xc+9.2c,8c + xc = .92 xc + 9.2 c,

and cc cancels! We find that

8+x=.92x+9.2,8 + x = .92 x + 9.2,

−08x=1.2,-08 x = 1.2,

x=15.x = 15.

The original profit was (b) 1515 percent.