Correct Answer - Option 2 : 55.5%

**Concept:**

**Dry density of soil:**

\(Dry\;density\;\left( {{γ _{dry}}} \right) = \frac{{{G}.{γ _w}}}{{1 + e}}\)

Where, γ_{w} = Density of water

e = Void ratio of soil

**Relationship between e,s,w, and G**

**Se = wG**

**Calculation:**

Given, G = 2.70, γ_{w} = 1 gm/cm^{3}, w = 12 % = 0.12

Dry density = 1.705 gm/cm^{3}

\(Dry\;density\;\left( {{γ _{dry}}} \right) = \frac{{{G}.{γ _w}}}{{1 + e}}\)

\(1.705 = \frac{{{2.7}\ ×\ {1}}}{{1 + e}}\)

1 + e = 1.583

**e = 0.583**

Relationship between e,s,w, and G

Se = wG

S × 0.583 = 0.12 × 2.7

S = 0.555

**S = 55.5 %**