If a person covers the same distance by walking, by cycling and by running with speeds in the ratio 1: 9: 3 respectively, then the ratio of the ratios of their times and speeds of the three modes of travel is

Let say ,speed of walking, cycling and running are k,9k and 3k respectively.

Time and speed are inversely proportional when distance is constant.

So,their time taken would be as following:

(1/k),(1/9k) and (1/3k).

So,ratio of time and speed would be :

(1/k)/k ,(1/9k)/9k and (1/3k)/3k

or,$$(1/k^2), (1/81k^2) and (1/9k^2)$$.

So , required ratio would be ==>

$$(1/k^2):(1/81k^2):(1/9k^2)$$

=$$1:(1/81):(1/9)$$

=81:1:9.

C is correct choice.