The volume of 0.05 M H2SO4 is needed to completely neutralise 15ml of 0.1 M NaOH solution is

V (NaOH) = 15 mL = 0.015 L

C (NaOH) = 0.1 mol/L

C (H₂SO₄) = 0.05 mol/L

2NaOH + H₂SO₄ = Na₂SO₄ + 2H₂O

n (NaOH) = V (NaOH) C (NaOH) = 2n (H₂SO₄)

n (H₂SO₄) = V (H₂SO₄) C (H₂SO₄)

V (NaOH) C (NaOH) = 2V (H₂SO₄) C (H₂SO₄)

V (H₂SO₄) = V (NaOH) C (NaOH) / {2C (H₂SO₄) }

V (H₂SO₄) = 0.015*0.1/{2*0.05}=0.015 L = 15 mL