Question

What quantity of water (in ml) should be added to reduce glycerin content from 60% to 50% in a 320ml body lotion?

• A. 50ml
• B. 55ml
• C. 60ml
• D. 64ml

Hint:

In dilution problems where a solvent (like water) is added, the amount of the solute (the substance being diluted) remains constant. Use the formula: Initial Quantity of Solute = Final Quantity of Solute, which can be expressed as \( C_1V_1 = C_2V_2 \), where \( C \) is concentration and \( V \) is volume.

Answer 1

The Correct Option is D

Step 1: Calculate the initial quantity of glycerin in the body lotion. Given: Initial volume of body lotion = 320 ml Initial glycerin content = 60% Quantity of glycerin = Initial glycerin content \( \times \) Initial volume \[ \text{Quantity of glycerin} = 60% \times 320 \text{ ml} \] \[ \text{Quantity of glycerin} = \frac{60}{100} \times 320 \] \[ \text{Quantity of glycerin} = 0.6 \times 320 \] \[ \text{Quantity of glycerin} = 192 \text{ ml} \] So, there are 192 ml of glycerin in the original 320 ml body lotion. Step 2: Set up an equation for the final state after adding water. Let \( x \) ml be the quantity of water added to the body lotion. The total volume of the new solution will be \( (320 + x) \) ml. The glycerin content in the new solution is desired to be 50%. Since only water is added, the actual quantity of glycerin (192 ml) remains unchanged. In the new solution: Quantity of glycerin = Final glycerin content \( \times \) New total volume \[ 192 = 50% \times (320 + x) \] \[ 192 = \frac{50}{100} \times (320 + x) \] \[ 192 = 0.5 \times (320 + x) \] Step 3: Solve the equation to find the quantity of water added (\( x \)). \[ 192 = 0.5 \times (320 + x) \] Divide both sides by 0.5: \[ \frac{192}{0.5} = 320 + x \] \[ 384 = 320 + x \] Subtract 320 from both sides: \[ x = 384 - 320 \] \[ x = 64 \text{ ml} \] Therefore, 64 ml of water should be added to reduce the glycerin content from 60% to 50%.