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Ratio problem

  1. Dec 14, 2009 #1
    I am having difficulty with this problem and I was wondering if anyone can talk me through it?

    Mr Smith starts a business with $50,000.
    3 months later, Mr Jones joins the business. He invests $25,000
    The profit at the end of the year is $11,000. It is divided in proportion to how much was invested and for how long.

    I know that I have to express the $11,000 as a fraction which can then be divided between the 2 men accordingly, but I have no idea how to achieve that! Can anyone help?
  2. jcsd
  3. Dec 14, 2009 #2


    Staff: Mentor

    If both Smith and Jones had made their investments at the start of the year, the problem would be a lot easier. In that case, they would split the profit in the ratio 2:1, with Smith getting 2/3 of the profit and Jones getting 1/3 of the profit.

    The complication is that Jones made an investment for only 3/4 of the year, while Smith's investment was for the entire year. One solution would be to reduce Jones's profit by 25% and add that amount of money to Smith's share. Note that you can't simply reduce Jones's share of the profit by 25% and increase Smith's share by 25%. The base amounts are different, so you would be adding more money to Smith's share than was subtracted from Jones's share.
  4. Dec 14, 2009 #3
    The way I would go about it is to say Smith has invested $50,000 for 12 months, multiplying gives 600,000.

    Jones has invested $25,000 for 9 months, multiplying gives 225000. Divide $11,000 by the sum of these, and then multiply by 600000 for Smith's share and 225000 for Jones' share
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