An Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE &
CBSE Board.
Here Given :
(i)Chemist solutions containing acid in percentage
You have to find how much of each should be used to make 10 litres of a 40% acid solution.
This is the Question Number 53 Exercise 3E of RS Aggarwal Solution.
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A chemist has one solution containing 50% acid and a second one containtng 25% acid. How much of each should be used to make 10 litres of a 40% acid solution?
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Let the amount of 50% acid be x liters.
And the amount of 25% acid be y litres.
To make 10 litres of 40% acid solution,
0.5x+0.25y=4———-(i)
x+y=10————–(ii)
[balancing concentrations]
Multiply the equation (i) by 10.
Then the equation (i) becomes,
(i)x10=5x+2.5y=40———-(iii)
And multiply the equation (ii) by 5
Then the equation (ii) becomes,
(ii)x5=5x+5y=50———(iv)
By subtracting, equation (iii) from (iv)
Subtracting,
5x+2.5y=40
5x+5y=50
-2.5y=-10
Then,
y=10/2.5=4
Substituting the value of y, (y = 4) in equation (iii) we get,
5x+2.5y=40
5x+2.5(4)=40
5x+10=40
5x=30
x=6
Hence, 6 litres of 50% solution and 4 litres of 25% solution are needed to form 10 litres of 40% of acid solutions.