Question

How many litres of $20$% of alcohol solution to be added to $40$ litres of $50$% alcohol solution to make a $30$% solution?

Answer 1

Let $x$ be the quantity of the 20% alcohol solution to be added to the 40lts. of a 50% alcohol and let $y$ be the quantity of the final30% solution, so we get the equation as,
$x+40=y$
Keeping in mind that here the alcohol is to be taken in terms of percentage we get the equation as,
20%$x$+50%$\times$40=30%$y$
Now by substituting the value of $y$ in terms of $x$ we get
20%$x$+50%$\times$40=30%$(x+40)$
If we convert the percentage in fractions and then multiply all the terms by 100 or in simple language, if we remove the percent sign from al the terms we get this equation as,
$20x+50\times 40=30x+30\times 40$
$30x-20x=2000-1200$
$10x=800$
$x=80$
Answer : 80lts. of 20% alcohol is to be added to 40lts. of alcohol with 50% percent in order to make a solution of 30% of alcohol.
Ans ; 80