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ktzsikka
What was the percentage discount given on the marked price of an item?

(1) The marked price of the item is 20 percent more than the cost price.
(2) The selling price of the item after the discount is equal to $2,000.

Solution:
Pre Analysis:
  • We are asked the discount percentage given on MP of an item

Statement 1: The marked price of the item is 20 percent more than the cost price
  • According to this statement, \(MP=(1+\frac{20}{100})CP\) or \(MP=1.2CP\)
  • However, this will not be enough to get the discount percentage d
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: The selling price of the item after the discount is equal to $2,000
  • Accoriding to this statement, \(SP=$2000\)
  • We know \(SP=MP(1-\frac{d}{100})\)
    \(⇒2000=MP(1-\frac{d}{100})\)
  • This, however, will not get us the value of \(d\) without the value of MP
  • Thus, statement 2 alone is also not sufficient

Combining:
  • From statement 1, we get \(MP=1.2CP\)
  • From statement 2, we get \(2000=MP(1-\frac{d}{100})\)
  • Upon combining, we can write \(2000=1.2CP(1-\frac{d}{100})\)
  • We still cannot get the value of \(d\) without the value of CP or MP

Hence the right answer is Option E
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