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Math Help - Profit Loss Problem

  1. #1
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    Question Profit Loss Problem

    Albert sells a cycle to Ben at a profit of 20% & Ben sells it to Cindy at a profit of 25%. If Cindy pays $1500, what did Albert pay for it?

    This is how I tried:

    Let Cost Price (C.P.) of Albert be 100

    Profit Percentage of Albert=20%
    So Selling Price (S.P.) of Albert (to Ben)=100+(20% of 100)=120

    Profit Percentage of Ben=25%
    So S.P. of Ben (to Cindy)=120+(25% of 120)=150

    Now how do I proceed ahead?

    Thanks,

    Ron
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Well, while you picked the lucky ticket but didn't know how to use it, I'd have done it using what I know.

    The CP to Cindy is $1500.

    Let the cost price of Ben be x.

    To find the selling price of Ben, we need x + (\dfrac{20}{100})x

    So, we get:

    x + (\dfrac{25}{100})x = 1500

    Find x.

    Then, do the same. Let y for example be the cost price of Albert. The selling price of Albert is given by:

    y + (\dfrac{20}{100})y
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  3. #3
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    OK...this is how I tried it.....

    Let Ben's CP be 100
    So Ben's SP=100+(25% of 100)=125

    Ben's SP=Cindy's CP=1500

    If Ben's SP=125, Ben's CP=100
    If Ben's SP=1500, Ben's CP=(1500X100)/125=1200

    Let Albert's CP be 100
    So Albert's SP=100+(20% of 100)=120

    Albert's SP=Ben's CP=1200

    If Albert's SP=120, Albert's CP=100
    If Albert's SP=1200, Albert's CP=(1200x100)/120=1000

    So Albert pays $1000 for the cycle.

    Have I done it correctly (answer is correct)? Are the steps correct?

    Thanks,

    Ron
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  4. #4
    MHF Contributor Unknown008's Avatar
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    The answers are correct. As for the method, I'm not sure if it is accepted, but I understand the logic behind it.
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