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
$\therefore 30\%$ 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 $\frac{30x}{100}+\frac{12}{100}\left(600\right)>\frac{15}{100}\left(x+600\right)$
and $\frac{30x}{100}+\frac{12}{100}\left(600\right)<\frac{18}{100}\left(x+600\right)$
or $30x+7200>15x+9000$
and $30x+7200<18x+10800$
or $15x>1800$ and $12x<3600$
or $x>120$ 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.