This question is from linear equations in two variables in which we have given that if 90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. Then we have to find how many litres of each solution are mixed?
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3E, question no 50
Let quantity 90% pure acid is x litre and 97% pure acid solution is y litre
Then x+y=21………………………………………………………………(1) (given)
And x×90/100+y×97/100=(x+y)×95/100
⇒90x+97y=95(x+y)⇒90x−97y=95x+95y
⇒90x−95x+97y−95y=0
⇒−5x+2y=0…………………………………….(2)
Multiply (1) by 2 we get
2x+2y=42.……………………………………………………………….(3)
Substructure (2) with (3) we get
7x=42
Or x=6
Put the value of x=6 in equation (1) we get
7+y=21
Or y=21−6=15
Then 90% pure acid is 6 liters and 97 % pure acid is 15liters