Identify the relevant soil mechanics relationship

The relationship connecting degree of saturation ($S$), void ratio ($e$), water content ($w$), and specific gravity ($G$) in soil mechanics is given by the fundamental phase relation formula.

$Se = wG$

Substitute the given values into the formula

We have $e = 0.65$, $w = 0.20$, and $G = 2.72$. Substituting these into the formula to solve for $S$:

$S \times 0.65 = 0.20 \times 2.72$

Calculate the degree of saturation

Solving for $S$: $S = \frac{0.20 \times 2.72}{0.65} = \frac{0.544}{0.65} \approx 0.8369$. To express this as a percentage, multiply by 100.

$S \approx 83.69\%$

Rounding and result verification

Rounding the value to one decimal place as per the options provided, we get $83.7\%$.

$S = 83.7\%$