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

The Correct Option is C

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