A manufacturer has 600 litres of 12 acidic solution

Asked by admin @ 23/08/2021 in Math viewed by 360 People

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 contains in resulting mixture will be more than 15% but less than 18%

Answered by admin @ 23/08/2021

Let's "x" liters of 35% acid solution is required to be added

Then

Total mixture = (x + 600) liters.

Therefore ,

$30\% \: x \: + 12\% \: of \: 600 > 15\% \: of \: (x + 600) \\ \\ = > \frac{30x}{100} + \frac{12}{100} \times 600 \: > \: \frac{15}{100} (x + 600) \\ \\ = > 30x + 7200 > 15x + 9000 \\ \\ = > 15x > 1800 \\ \\ = > x > 120$
_______________________________

AND

$30\% \: x + 12\% \: of \: 600 < 18 \% \: of \: (x + 600) \\ \\ = > \frac{30x}{100} + \frac{12}{100} \times 600 < \frac{18}{100} (x + 600) \\ \\ = > 30x + 7200 < 18x + 10800 \\ \\ = > 12x < 3600 \\ \\ = > x < 300$
______________________________

so

$= > 120 < x < 300$
____________________[ANSWER]

Thus, the no. of liters of the 30% solutions of acid will have to be more than 120 liters but less then 300 liters.

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_-_-_-_☆ $BE \: \: \: \: BRAINLY$ ☆_-_-_-_

A manufacturer has 600 litres of 12 acidic solution

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