Question

A manufacturer has $600$ litres of a $12\%$ solution of acid. How many litres of a $30\%$ acid solution must be added to it so that acid content in the resulting mixture will be more than $15\%$ but less than $18\%$?

• A. more than $120$ litres but less than $300$ litres
• B. more than $140$ litres but less than $600$ litres
• C. more than $100$ litres but less than $280$ litres
• D. more than $160$ litres but less than $500$ litres

Answer 1

Answer: (A)

Let $x$ litres of $30\%$ acid solution is required to be added. Then
Total mixture $= (x + 600)$ litres
$\therefore \quad30\%$ of $x + 12\%$ of $600 > 15\%$ of $\left(x + 600\right)$
and $30\%$ of $x + 12\%$ of $600 < 18\%$ of $\left(x + 600\right)$
or $\quad \frac{30x}{100} + \frac{12}{100} \left(600\right) > \frac{15}{100} \left(x + 600\right)$
and $\quad\frac{30x}{100} + \frac{12}{100} \left(600\right) < \frac{18}{100} \left(x + 600\right)$
or $\quad30x + 7200 > 15x + 9000$
and $30x + 7200 < 18x + 10800$
or $\quad15x > 1800$ and $12x < 3600$
or $\quad x > 120$ and $x < 300$.
i.e., $120 < x < 300$
Thus, the number of litres of the $30\%$ solution of acid will have to be more than $120$ litres but less than $300$ litres.