Question

A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25%?

• A. More than 100 litres but less than 300 litres
• B. More than 120 litres but less than 400 litres
• C. More than 100 litres but less than 400 litres
• D. More than 120 litres but less than 300 litres
• E. None of the above

Hint:

For mixture problems with percentage range, always set up inequalities for lower and upper limits and solve step by step.

Answer 1

The Correct Option is C

Step 1: Define quantities.
We have 200 litres of 15% acid solution.
Let $v$ litres of 30% acid solution be added.
Total mixture = $200 + v$ litres.
Total acid = $0.15 \times 200 + 0.30 \times v = 30 + 0.30v$.
Step 2: Express the condition.
We need the acid percentage in the mixture to be between 20% and 25%.
So, \[ 20%<\frac{30 + 0.30v}{200 + v}<25% \] Step 3: Solve lower bound (20%).
\[ \frac{30 + 0.30v}{200 + v}>0.20 \] \[ 30 + 0.30v>0.20(200 + v) = 40 + 0.20v \] \[ 0.10v>10 \quad \Rightarrow \quad v>100 \] Step 4: Solve upper bound (25%).
\[ \frac{30 + 0.30v}{200 + v}<0.25 \] \[ 30 + 0.30v<0.25(200 + v) = 50 + 0.25v \] \[ 0.05v<20 \quad \Rightarrow \quad v<400 \] Step 5: Conclude.
Therefore, the volume of 30% acid solution to be added must be between 100 and 400 litres. \[ \boxed{\text{More than 100 litres but less than 400 litres (Option C)}} \]