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Standard X

Mathematics

Method of Substitution to Find the Solution of a Pair of Linear Equations

90% and 97% p...

Question

90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution.Find the quantity of each type of acids to be mixed to form the mixture.

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Solution

$V_{1}$ = volume of 90% solution
$V_{2}$ = volume of 97% solution

Volume of solution $= V_{1} + V_{2} = 21 L$

Concentration $= 95 % = \frac{(V_{1} \times 90 % + V_{2} \times 97 %)}{21}$

So $21 \times 95 = 90 V_{1} + 97 V_{2}$

$= 90 V_{1} + 97 (21 - V_{1}) = 97 \times 21 - 7 V_{1}$

So $V_{1} = 6 L$ and $V_{2} = 15 L$

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Q. 90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution.
Find the quantity of each type of acids to be mixed to form the mixture.

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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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90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution.Find the quantity of each type of acids to be mixed to form the mixture.

V1= volume of 90% solution V2= volume of 97% solution Volume of solution =V1+V2=21L Concentration =95%=(V1×90%+V2×97%)21 So 21×95=90V1+97V2 =90V1+97(21−V1)=97×21−7V1 So V1=6L and V2=15L