Question

A manufacturer has 600 L of a 12% solution of acid. How many litres of a 30% acid solution must be added to it such that acid content in the resulting mixture will be more than 15% but less than 18%?
1.  more than 120 L but less than 300 L
2.  more than 140 L but less than 320 L
3.  more than 110 L but less than 290 L
4.  more than 220 L but less than 300 L

Answer 1

Correct Answer - Option 1 :  more than 120 L but less than 300 L

Given:

Volume = 600 L

Content of Acid = 12%

Content of Acid in the newly added solution = 30%

Acid Content range of the new resulting mixture = 15% to 18%

Calculation:

Assume, X liter amount was added to the 600 L solution.

New volume of the mixture = (600 + X) liter

According to the given condition,

15% of New mixture volume < (Old + Added) Acid content < 18% of New mixture volume

= 15% of (X + 600) < (12% of 600 + 30% of X) < 18% of (X + 600)

\(\Rightarrow \dfrac{15}{100}\times (600+X)< \dfrac{12}{100}\times (600) + \dfrac{30}{100}\times (X) < \dfrac{18}{100}\times (600+X)\)

\(\Rightarrow \dfrac{15}{100}\times (600+X) < \dfrac{7200}{100} + \dfrac{30}{100}\times (X) < \dfrac{18}{100}\times (600+X)\)

Dividing by 100, we get

= 9000 + 15X < 7200 + 30X < 10800 + 18X

Solving this we get.

= 15X > 1800 and 12X < 3600

= X > 120 and X < 300

Hence, the added volume should be more than 120 L but less than 300 L.