A cyclist drove one kilometre, with the wind in his back, in 3 minutes and drove the same way back, against the wind, in 4 minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive 1 km without wind ?

Answer: Option C

Let the cyclist's speed without wind be x km/hr
And the speed of the wind be y km/hr
Then,
$$\begin{array}{rl}& \Rightarrow \frac{1}{x+y}=\frac{3}{60}\\ & \Rightarrow x+y=\mathrm{20.....}(i)\end{array}$$
And
$$\begin{array}{rl}& \Rightarrow \frac{1}{x-y}=\frac{4}{60}\\ & \Rightarrow x-y=\mathrm{15.....}(ii)\end{array}$$
Adding (i) and (ii), we get:
2x = 35 or x = 17.5
Putting x = 17.5 in (i), we get : y = 2.5
Time taken to drive 17.5 km without wind = 1 hr
Time taken to drive 1 km without wind
$$\begin{array}{rl}& =\left(\frac{1}{17.5}\right)\text{ hr}\\ & \text{ = }\left(\frac{1}{17.5}\times 60\right)\text{ min}\\ & \text{ = 3}\frac{3}{7}\text{ min}\end{array}$$