Dilfuza owns a small clothing shop in Namangan. In September she bought 150 summer dresses from a wholesaler at 40 dollars each. As usual, the dresses were marked up by 50 percent, so each one went on the rack at 60 dollars.
The weather turned cold early, and the dresses did not sell. By November, all 150 were still in the storeroom. Her assistant suggested a clearance sale and put a large sign in the window: 40 percent off the marked price.
The sign worked, and the dresses were gone in a week. Dilfuza was pleased until she did the accounts. Forty percent off 60 dollars is 24 dollars, so each dress sold for 36 dollars, four dollars less than it had cost. On 150 dresses, the sale had lost 600 dollars.
Her assistant was surprised. "We added fifty percent and took off only forty," she said. "Shouldn't we still be ten percent ahead?" Dilfuza explained that the two percentages were taken from different prices. The markup was half of 40 dollars, but the discount was four tenths of 60 dollars. One and a half times six tenths is nine tenths, so the sale price was only 90 percent of the cost: a ten percent loss, not a ten percent profit.
For the next clearance, Dilfuza set a rule. The largest discount the shop can give without losing money on a 50 percent markup is one third, because one and a half times two thirds is exactly one. Anything more, and the shop pays its customers to take the clothes away.