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. $270B. $250C. $240D. $220E. $200

Option (A) $270

Step-by-step explanation:

Let the original cost store paid for the clock be $100

Thus,

According to the question:

Clock store sold to the collector for price = $100 + 20% of $100

= $100 + $20

= $120

Therefore,

The store bought back from the collector at a price = 50% of $120

= $60

Thus,

Store will sell back the clock for price = $60 + 80% of $60

= $60 + $48

= $108

Now,

Difference between original cost and buy back price

= $100 - $60

= $40

But,

The actual difference given in the question = $100

i. e 2.5 times $40

Hence,

The shop sold the clock a second time for the price

= 2.5 * $108

= $270

Option (A) $270