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