Question

A manufacturer has $500\text{ }L$ of a $10\%$ solution of acid, find the range of 40% acid to be added to it , such that the acid content in the resultant mixture will be more than $15\%$ but less than $20\%$ .

• A. More than $250\text{ }L$ and less than $~300$
• B. More than $300\text{ }L$ and less than $400$
• C. More than $100\text{ }L$ and less than $250$
• D. More than $250\text{ }L$ and less than $350$

Answer 1

Answer: (C)

More than $100\text{ }L$ and less than $250$

Answer 2

Let x litre of 40% acid solution is required to be added. Then, Total mixture
$=(x+500)L$
$\therefore$ $40$% of $x+10$% of $500>15$% of $(x+500)$
$\Rightarrow$ $\frac{40x}{100}+\frac{10\times 500}{100}>\frac{15}{100}\times (x+500)$
$\Rightarrow$ $40x+5000>15x+7500$
$\Rightarrow$ $25x>2500$
$\Rightarrow$ $x>100$ ..(i) Also, $40$ of $x+10$ of $500<20$ of $(x+500)$
$\Rightarrow$ $ \frac{40}{100}x+\frac{10}{100}\times 500