An important and exam oriented question from linear equations in two variables in which we have given that a chemist has one solution containing 50% acid and a second one containing 25% acid. We have been asked to find how much of each should be mixed to make 10 litres of a 40% acid solution.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 49

Let X be the amount of first solution and Y be the amount of second to be taken.

The amount of acid in x=0.5x

But another 50% has to be water.

The amount of water =0.5x.

The amount of acid in y=0.25y

The amount of water in y=0.75y

The total amount of acid required in final solution =0.4×10=4 litres and remaining 6 lit would be water.

Therefore,

0.5x+0.25y=4 ………….(1)

Or,0.5x=4−0.25y

Similarly for water,

0.5x+0.75y=6 ……………..(2)

Substituting the value of 0.5x from Eq. (1) into Eq. (2) we have,

4−0.25y+0.75y=6

4+0.5y=6

y=4

x=6