For a liquid, the permeability of a sandy soil having a void ratio of 0.60 was determined as 0.14 cm/s. Considering the same liquid and by using Taylor’s equa tion, the permeability (in cm/s) of this soil corresponding to the void ratio of 0.80 is _______(rounded off to two decimal places).

The correct option is 0.29.

To find the permeability of the sandy soil at a different void ratio, we can use Taylor's relation. According to Taylor's equation, the coefficient of permeability ($k$) of a sandy soil is directly proportional to a function of its void ratio ($e$):
$k\propto \frac{e^3}{1+e}$
where $e$ is the void ratio of the soil.

Let the initial state of the soil be represented by:
Void ratio, $e_1=0.60$
Permeability, $k_1=0.14\text{cm/s}$

Let the final state of the soil be represented by:
Void ratio, $e_2=0.80$
Permeability, $k_2$ (to be determined)

From the proportionality relation, we can establish the ratio:
$\frac{k_2}{k_1}=\frac{e_2^3/(1+e_2)}{e_1^3/(1+e_1)}$
Rearranging this equation to solve for $k_2$:
$k_2=k_1\times {\left(\frac{e_2}{e_1}\right)}^3\times \left(\frac{1+e_1}{1+e_2}\right)$

Now, substitute the given values into the equation:
$k_2=0.14\times {\left(\frac{0.80}{0.60}\right)}^3\times \left(\frac{1+0.60}{1+0.80}\right)$
Simplifying the terms inside the parentheses:
${\left(\frac{0.80}{0.60}\right)}^3={\left(\frac{4}{3}\right)}^3=\frac{64}{27}\approx 2.3704$
$\frac{1+0.60}{1+0.80}=\frac{1.60}{1.80}=\frac{8}{9}\approx 0.8889$

Substituting these values back into the main expression:
$k_2=0.14\times 2.3704\times 0.8889$
$k_2\approx 0.14\times 2.1070$
$k_2\approx 0.29498\text{cm/s}$

Rounding off the calculated permeability to two decimal places yields:
$k_2\approx 0.29\text{cm/s}$