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# 90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed?

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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

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1. ## 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)90x97y=95x+95y

90x95x+97y95y=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=216=15
Then 90% pure acid is 6  liters and 97 % pure acid is 15liters

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