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