Question

How many liters of water will have to be added to 1125 liters of 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

• A. More than 600 liters but less than 800 liters
• B. 600 liters से अधिक तथा 800 liters से कम
• C. More than 550 liters but less than 700 liters
• D. More than 562.5 liters but less than 900 liters

Hint:

For mixture problems, use percentage concentration equations and solve inequalities to find the required range of added water.

Answer 1

The Correct Option is D

Step 1: Define variables
Let the amount of water to be added be \( x \) liters. The total amount of acid in the solution initially is: \[ 0.45 \times 1125 = 506.25 \text{ liters} \] After adding \( x \) liters of water, the total volume becomes: \[ 1125 + x \text{ liters} \] Step 2: Set up inequalities based on the required acid percentage
We want the acid concentration to be between 25% and 30%, so: \[ 0.25 \times (1125 + x) < 506.25 < 0.30 \times (1125 + x) \] Step 3: Solve for \( x \)
Solving the lower bound: \[ 506.25 > 0.25 \times (1125 + x) \] \[ \frac{506.25}{0.25} > 1125 + x \] \[ 2025 > 1125 + x \] \[ x < 900 \] Solving the upper bound: \[ 506.25 < 0.30 \times (1125 + x) \] \[ \frac{506.25}{0.30} < 1125 + x \] \[ 1687.5 <1125 + x \] \[ x > 562.5 \] Thus, the range of \( x \) is: \[ 562.5 < x < 900 \] Therefore, the correct answer is more than 562.5 liters but less than 900 liters.