Get Answers to all your Questions

header-bg qa

Q12.    A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Answers (1)

best_answer

Let x litres of 2% boric acid solution is required to be added.

Total mixture = (x+640) litres 

The resulting mixture is to be more than 4% but less than 6% boric acid.

\therefore \, 2\%x+8\%\, of\, 640> 4\%\, of\, (640+x)                    and       2\%x+8\%\, of\, 640< 6\%\, of\, (x+640)  

\Rightarrow \, 2\%x+8\%\, of\, 640> 4\%\, of\, (640+x)                  and      2\%x+8\%\, of\, 640< 6\%\, of\, (x+640)

\Rightarrow \, \frac{2}{100}x+(\frac{8}{100}) 640> \frac{4}{100} (640+x)                                 \Rightarrow \, \frac{2}{100}x+(\frac{8}{100}) 640< \frac{6}{100} (640+x)

\Rightarrow \, 2x+5120> 4x+2560                                                        \Rightarrow \, 2x+5120< 6x+3840

\Rightarrow \, 5120-2560> 4x-2x                                                       \Rightarrow \, 5120-3840< 6x-2x

\Rightarrow \, 2560> 2x                                                                                   \Rightarrow \, 1280< 4x

\Rightarrow \, 1280> x                                                                                     \Rightarrow \, 320< x

Thus, the number of litres  2% of boric acid solution that is to be added will have to be more than 320 and less than 1280 litres.

 

 

 

 

 

 

 

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads