A solution contains 30% alcohol by weight.How much more alcohol must be added to 100g of the solution so that the percentage of alcohol may become 50%?   

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tiburtius's profile pic

tiburtius | High School Teacher | (Level 2) Educator

Posted on

We can calculate mass percentage of alcohol in a solution this way

`p=(100m_a)/m_s`

where `m_a` is mass of alcohol, `m_s` ` `  is mass of whole solution and `p` is percentage.

So if solution of 100g contains 30% of alcohol it follows that

`30=(100 m_a)/100`

`m_a=30`g  <-- current mass of alcohol in the solution

Now to get solution with 50% of alcohol we will add `x` grams of alcohol so we have

`50=(100(30+x))/(100+x)`

`0.5=(30+x)/(100+x)`

`50+0.5x=30+x`

`-0.5x=-20`

`x=40"g"`

So we need to add 40g of alcohol to the solution to get solution with 50% of alcohol.

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

Alcohal in 100 solution is= 30%100=30g

let x grams alcohoal added to solution to make it 50% alcohol.

by given condition

50% of (100+x)=30+x

100+x=60+2x

100-60=2x-x

40=x

40g  alcohal must be added to make 50% solution.

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