Question

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

Answer 1

Let us assume x % of acid to be added ,then

Total mixture $=(x+600)$ litres

Therefore

$30\%x+12\%of600>15\%of(x+600)$

and $30\%x+12\%of600<18\%of(x+600)$

$\frac{30x}{100}+\frac{12}{100}\left(600\right)>\frac{15}{100}(x+600)$

and $\frac{30x}{100}+\frac{12}{100}\left(600\right)<\frac{18}{100}(x+600)$

$30x+7200>15x+9000$

and $30x+7200<18x+10800$

$15x>1800\&12x<3600$

$x>120\&x<300$

Thus the no of 30% solution acid should be more than 120 litres but less than 300 litres