Find the ratio of swimming speed of Vikash in still water to speed of river, if ratio of time taken to go 5 Km upstream to time taken to go 5 km downstream is 10 : 5 ?

3 : 1

⇒ When distance is same, then the relation between speed and time is inverse.

Here, Distance = 5 km

So, Speed ∝ \(\frac{1}{time}\)

⇒             Upstream(U)  :   Downstream(D)

Time    :            10           :            5

Speed  :            5            :           10     

                          1           :           2

Speed of boat in still water = \(\frac{S_D\;+\;S_U}{2}\) = \(\frac{2\;+\;1}{2}\) = \(\frac{3}{2}\)

Speed of current = \(\frac{S_D\;-\;S_U}{2}\) = \(\frac{2\;-\;1}{2}\) = \(\frac{1}{2}\)

Required ratio = \(\frac{3}{2}\) : \(\frac{1}{2}\) = 3 : 1