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.