Question

$90\%$ 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?

• A. $2$ litres and $14$ litres
• B. $8$ litres and $35$ litres
• C. $7$ litres and $25$ litres
• D. $6$ litres and $15$ litres

Answer 1

The correct option is D $6$ litres and $15$ litres

Let quantity $90$% pure acid is $x$ litre and $97$% pure acid solution is $y$ litre

Then $x+y=21$........................................................................(1) (given)

And $x\times \frac{90}{100}+y\times \frac{97}{100}=(x+y)\times \frac{95}{100}$

$\Rightarrow 90x+97y=95(x+y)\Rightarrow 90x-97y=95x+95y$

$\Rightarrow 90x-95x+97y-95y=0$

$\Rightarrow -5x+2y=0$...........................................(2)

Multiply (1) by 2 we get

$2x+2y=42.$.........................................................................(3)

Substructure (2) with (3) we get

$7x=42$

Or $x=6$

Put the value of $x=6$ in equation (1) we get

$7+y=21$

Or $y=21-6=15$

Then $90\%$ pure acid is $6$ liters and $97$ pure acid is $15$liters