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Briefcase problem

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data
    A briefcase was sold at a profit of 10%.If the cost price was 5% less and it was sold for $ 7 more , the gain would have been 20% .Find the cost price of briefcase.

    2. The attempt at a solution
    I assumed cost price to be x
    for 10% gain selling price would be 11x/10
    & for 20 % gain selling price would be 6x/5 and profit would be x/5
    by the condition 3x/20 +7= x/5 =>where x= 140
    But the book's answer is $175
    I don't know where i am going wrong and also each time the answers are coming different.
    Please help me to rectify where i am going wrong .
    thank you.
  2. jcsd
  3. Jan 23, 2010 #2


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    Hi 1/2"! :smile:

    No, it means the gain over the new cost price would be 20%. :wink:

    (and where did 3/20 come from?)
  4. Jan 23, 2010 #3
    Start with the cost of the briefcase = X dollars
    It was sold for S dollars.
    Since there was a profit, we know S>X and the amount of the profit was S-X dollars.

    The percent of profit is found by dividing the profit by the cost, so

    [tex]\frac{S-X}{X} = 10\% = 0.1[/tex]

    Solving for S, you can see that it sold for 1.1X dollars.

    Now, if the cost of the briefcase was 5% lower (X-0.05X = 0.95X dolllars)
    and, if it sold for $7 more (S+7, or 1.1X + 7 dollars)
    then the profit would have been 20%.

    So the actual profit would then have been (1.1X + 7) - 0.95X dollars.

    Dividing by the cost gives the percent gain:

    [tex]\frac{1.1X + 7 - 0.95X}{0.95X} = 20\% = 0.2[/tex]
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