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Math Help - Proportion again !!!

  1. #1
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    Smile Proportion again !!!

    A couple of questions..

    1. Four friends P,Q,R,S are working on an assignment together. They contribute to the work in the ratio 1:2:3:4 respectively. They can complete the work individually in 1,2,3,4 days respectively. If they work one after the other , how many days does it take to complete the assignment ?

    2. The weights of 3 heaps of gold are in the ratio 5:6:7. By what fractions of themselves must the first two be increased so that the ratio of the weights is changed to 7:6:5 ?

    ans : 24/25 , 2/5
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  2. #2
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    Hello, MathLearner!

    2. The weights of 3 heaps of gold are in the ratio 5:6:7.
    By what fractions of themselves must the first two be increased
    so that the ratio of the weights is changed to 7:6:5 ?

    Ans: \frac{24}{25},\;\;\frac{2}{5}

    The original weight are: . \{5a,\;6a,\;7a\}\;\;{\color{blue}[1]}

    The new weights are: . \{7b,\;6b,\;5b\}\;\;{\color{blue}[2]}

    The third weight is not changed: . 7a \:=\: 5b\quad\Rightarrow\quad b \:= \:\frac{7}{5}a

    Substitute into [2]: . \left\{7\left(\frac{7}{5}a\right),\;6\left(\frac{7  }{5}a\right),\;5\left(\frac{7}{5}a\right)\right\} \;=\;\left\{\frac{49}{5}a,\;\frac{42}{5}a,\;7a\rig  ht\}


    The first weight went from 5a\text{ to }\frac{49}{5}a, an increase of: . \frac{49}{5}a -5a \:=\:\frac{24}{5}a
    . . The fraction of increase is: . \frac{\frac{24}{5}a}{5a} \:=\:\boxed{\frac{24}{25}}

    The second weight went from 6a to \frac{42}{5}a, an increase of: . \frac{42}{5}a - 6a \:=\:\frac{12}{5}a
    . . The fraction of increase is: . \frac{\frac{12}{5}a}{6a} \:=\:\boxed{\frac{2}{5}}

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  3. #3
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    Thank You Sorobon !!!
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