A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?
$270
$250
$240
$220
$200


Solution:
If p is the price that the shop originally paid for the clock, then the price that the collector paid was 1.2p (to yield a profit of 20%). When the shop bought back the clock, it paid 50% of the sale price, or (.5)(1.2)p = .6p. When the shop sold the clock again, it made a profit of 80% on .6p or (1.8)(.6)p = 1.08p.

The difference between the original cost to the shop (p) and the buy-back price (.6p) is $100.
Therefore, p – .6p = $100. So, .4p = $100 and p = $250.

If the second sale price is 1.08p, then 1.08($250) = $270. (Note: at this point, if you recognize that 1.08p is greater than $250 and only one answer choice is greater than $250, you may choose not to complete the final calculation if you are pressed for time.)

I got this question while doing my 4th MGMT CAT.
As per the question the second sale price is increased by 80% but in your answer the second sale price is multiplied buy 1.08 which is 8% and not 80%.

Did i misunderstood some fine points or there is mistake in the explanation? pls do let me know.
regards,
Karthyk

the sales price increased by 80% over the .6*p cost. an increase by 80% of course means multiple by 1.8, so when we do that we get 1.8*.6*p = 1.08p. i hope this clears things up..

_________________
Tim Sanders
Manhattan GMAT Instructor