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Question
90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution. Find the quantity of each type of acid to be mixed to form the mixture.
Solution
Let x litres and y litres be respectively the amount of 90% and 97% pure acid solutions.
As per the given condition
0.90x + 0.97y = 21 × 0.95
⇒ 0.90x + 0.97y = 21 × 0.95 ……….(i)
And
x + y = 21
From (ii), substitute y = 21 – x in (i) to get
0.90x + 0.97(21 – x) = 21 × 0.95
⇒ 0.90x + 0.97× 21 – 0.97x = 21 × 0.95
⇒ 0.07x = 0.97× 21 – 21 × 0.95
`⇒ x =( 21 × 0.02)/ 0.07= 6`
Now, putting x = 6 in (ii), we have
6 + y = 21 ⇒ y = 15
Hence, the request quantities are 6 litres and 15 litres.
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