Question

$37.85\%$ and $92\%$ alcoholic solutions are mixed to get $35$ liters of an $89\%$ alcoholic solution. How many liters of each solution are there in the new mixture?

• A. $10$ L of the $1^{st}$, $25$ L of the $2^{nd}$
• B. $20$ L of the $1^{st}$, $15$ L of the $2^{nd}$
• C. $15$ L of the $1^{st}$, $20$ L of the $2^{nd}$
• D. None

Answer 1

The correct option is D None

Let $x$ litres of the $37.85\%$ alcoholic solution and $(35-x)$ litres of $92\%$ alcoholic solution be required to get $35$ L of $89\%$ solution.

Then $37.85\%$ of $x+92\%$ of $(35-x)=89\%$ of $35$
$\Rightarrow \frac{37.85x}{100}+\frac{92\times 35}{100}-\frac{92\times x}{100}=\frac{89}{100}\times 35$
$\Rightarrow 54.15x=105$

$\Rightarrow x=\frac{105}{54.15}=1.94L$ (approx)