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  • A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?

A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?

Answers (1)

Let us assume that ‘x’ litres of 3% solution is added to 460 L of 9% solution.

Thus, total solution = (460 + x)L

& total acid content in resulting solution = (460 × 9/100 + x × 3/100)

                                                            = (41.4 + 0.03x) %

Now, according to the question,

The resulting mixture we get should be less than 7% acidic & more than 5% acidic

Thus, we get,

5% of (460 + x) < 41.4 + 0.03x < 7% 0f (460 + x)

= 23 + 0.05x < 41.4 + 0.03x < 32.2 + 0.07x

Now,

23 + 0.05x < 41.4 + 0.03x           &          41.4 + 0.03x < 32.2 + 0.07x

= 0.02x < 18.4                         &        0.04x > 9.2

Thus, 2x < 1840                              &        4x > 920

= 230 < x < 920

Therefore, the solution between 230 l & 920 l should be added.
 

Posted by

infoexpert22

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