Two soil specimens with identical geometric dimensions were subjected to falling head permeability tests in the laboratory under identical conditions. The fall of water head was measured after an identical time interval. The ratio of initial to final water heads for the test involving the first specimen was 1.25. If the coefficient of permeability of the second specimen is 5 -times that of the first, the ratio of initial to final water heads in the test involving the second specimen is-

Correct option is C

The permeability of soil based on variable head test is given as:

Where
a is the area of standpipe
L is the length of the soil sample
Δt is the time taken for water in a standpipe to fall from height h1 to h2.
A  is the area of the soil sample
Let suffix ‘1’ denotes specimen 1 and suffix ‘2’ denotes specimen 2.
It is given that both specimens have identical geometric dimensions i.e. a, L, and A are the same for both specimens.
Therefore,