A solution whose volume is 80litres is made up of 40% of water and 60% of alcohol. When x litres of water are added, the...

      

A solution whose volume is 80litres is made up of 40% of water and 60% of alcohol. When x litres of water are added, the percentage of alcohol drops to 40%.
a)find the value of x
b)30litres of water is added to the new solution. Calculate the percentage of alcohol in the new solution
c)If 5litres of solution in (b) above is added to 2litres of the original solution ,calculate, in the simplest form, the ratio of water to that of alcohol in the resulting solution

  

Answers


Charles
In solving part (a)

First get the real volumes of water and alcohol
Water 40%*80=32ltrs
Alcohol 60%*80=48ltrs

Since only water was added the amount of alcohol didn't change bt only volume was dilute

48L=40%
XL=60%
Cross multiply and divide

(48L*60%)รท40% = 72L

X therefore is 40L
= 72-32=40L

IN SOLVING PART (b)

72L+30L=102L
Total volume=102L+48L=150L

%Alcohol=(48/150)*100=32%

IN SOLVING PART (c)

First get the volumes of water and alcohol in the 5L and 2L.
In 5L
Water=68% of 5L=3.4L
Alcohol=32% of 5L=1.6L
In 2L
Water=40% of 2=0.8L
Alcohol=60% of 2=1.2L
In the solution (7L)
Water= 3.4L+0.8L=4.2L
Alcohol= 1.6L+1.2L=3.8L
Calculation of ratios of water to alcohol
4.2:3.8
=42:38
Simplify
7:9

Charles W answered the question on December 26, 2017 at 09:33


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