Question

How many liters of $20\%$ alcohol solution should be added to $40$ liters of a $50\%$ alcohol solution to make a $30\%$ solution?

• A. $80$
• B. $70$
• C. $60$
• D. $50$

Answer 1

The correct option is A $80$

Let $x$ liters of $20\%$ alcohol solution,

$\Rightarrow$ $30\%=\frac{xof20\%+40of50\%}{x+40}$

$\Rightarrow$ $\frac{30}{100}=\frac{x\times \frac{20}{100}+40\times \frac{50}{100}}{x+40}$

$\Rightarrow$ $20x+2000=30(x+40)$

$\Rightarrow$ $20x+2000=30x+1200$

$\Rightarrow$ $10x=800$

$\Rightarrow$ $x=80$

$\therefore$ Required answer is $80$ liters.