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Math Help - Ratio and Proportion

  1. #1
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    Ratio and Proportion

    1) The income of A,B and C are in the ratio of 7:9:12 and their spending are in the ratio of 8:9:15. If A saves 1/4th of his income, then the savings of A, B,C are in the ratio of?

    2) A diamond falls down and breaks into three pieces whose weights are in the ratio 2:3:5. The value of diamond is proportionate to the square of it's weight. If the value of the original diamond is $20,000, what is the loss in value due to breakage?

    How do i solve these?
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  2. #2
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    Hello saberteeth
    Quote Originally Posted by saberteeth View Post
    1) The income of A,B and C are in the ratio of 7:9:12 and their spending are in the ratio of 8:9:15. If A saves 1/4th of his income, then the savings of A, B,C are in the ratio of?

    2) A diamond falls down and breaks into three pieces whose weights are in the ratio 2:3:5. The value of diamond is proportionate to the square of it's weight. If the value of the original diamond is $20,000, what is the loss in value due to breakage?

    How do i solve these?
    1) Consider a total income of 28\;(=7+9+12). Of this, A's income is 7 and he saves \frac14 of it. So he saves \frac74. He spends \frac34 of it; so he spends \frac{21}{4}.

    B's income is 9, and his spend is \frac98 of A's spend. So he spends \frac98\times\frac{21}{4}= \frac{189}{32}. Therefore he saves \left(9-\frac{189}{32}\right) = \frac{99}{32}.

    I'll leave you to work out C's spend and saving in the same way.

    When you've done that, write the savings as a ratio \frac{7}{4}:\frac{99}{32}: ..., and simplify the result. I reckon the final answer is 56:99:279.

    2) 2 + 3 + 5 = 10. So the weight of the smallest piece is \frac{2}{10}=0.2 of the weight of the original single diamond. So its value is the square of this fraction multiplied by the original value, which is:
    $ 0.2^2 \times 20,000 = $ 800
    Work out the value of the other two pieces in the same way. Add these values together, and subtract from $ 20,000 to find the total loss in value. I reckon the answer is $ 12,400.

    Grandad
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  3. #3
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    Quote Originally Posted by Grandad View Post
    When you've done that, write the savings as a ratio \frac{7}{4}:\frac{99}{32}: ..., and simplify the result.
    I reckon the final answer is 56:99:279.

    Grandad
    I make that 56:99:69
    Which one of us grandads is correct?

    224 288 384
    168 189 315
    === === ===
    056 099 069
    Last edited by Wilmer; December 5th 2009 at 07:27 AM. Reason: Add bottom li'l chart!
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  4. #4
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    Hello Wilmer
    Quote Originally Posted by Wilmer View Post
    I make that 56:99:78
    Which one of us grandads is correct?

    .
    I've just done it again, and got 56:99:69. So, if that's right, then neither of us was correct! (In my first attempt I dropped a digit and worked out 5\times21 instead of 15\times 21.)

    Do you agree?

    Grandad
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  5. #5
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    Yes, this grandad agrees...already edited my typo (AHEM!)
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  6. #6
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    Thank you!
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