Mixture density from mass conservation

Steps:

• Calculate mass of glycerine: 1.3 g/cm³ × 40 cm³ = 52 g.
• Let volume of water added be V cm³; its mass is 1 g/cm³ × V = V g.
• Total mass = 52 g + V g; total volume = 40 cm³ + V cm³.
• Set mixture density: (52 + V) / (40 + V) = 1.1; solve to get V = 80 cm³.

Why D is correct:

• 80 cm³ yields total mass 132 g and volume 120 cm³, so density = 132/120 = 1.1 g/cm³ exactly, per the conservation of mass formula.

Why the others are wrong:

• A: 40 cm³ gives density 92/80 = 1.15 g/cm³, too high.
• B: 44 cm³ gives density 96/84 ≈ 1.14 g/cm³, too high.
• C: 52 cm³ gives density 104/92 ≈ 1.13 g/cm³, too high.

Final answer: D