factor26 wrote: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?
a $270
b $250
c $240
d $220
e $200
answer is [/spoiler]a[spoiler] can someone please help me solve? [/spoiler]
We can guess and check.
Let the original cost = 100.
Sold at a 20% profit = 120.
Buy-back price = (1/2)*120 = 60.
Original cost - the buy-back price = 100-60 = 40.
Too small: the problem states that the difference between the original cost and the buy-back price is 100.
Since 100/40 = 5/2, all of the values determined above -- including the buy-back price -- must be multiplied by a factor of 5/2.
Thus:
Actual buy-back price = (5/2)*60 = 150.
Resold at an 80% profit = 150 + .8*(150) = 270.
The correct answer is
A.
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