The duration of the journey from your home to the College in the local train varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the diesel used per km., and inversely as the number of carriages in the train. If, in a journey of 70 km. in 45 minutes with 15 carriages, 10 litres of diesel is required, then the diesel that will be consumed in a journey of 50 km. in half an hour with 18 carriages is

Let D be the distance, T be the time, V be the velocity, N be the number of carriages and X be the liters of Diesel required.
Given T$$\ltimes \dfrac{D}{V}$$
Also given that, V $$\ltimes \dfrac{\sqrt{\frac{X}{D}}}{N}$$
Thus, T = $$\dfrac{k*N*D^{\frac{3}{2}}}{\sqrt{X}}$$
Given when in a journey of 70 km, in 45 minutes with 15 carriages, 10 litres of diesel is required
Thus, 45 = $$\dfrac{k*15*70^{\frac{3}{2}}}{\sqrt{10}}$$
Thus, k = $$\dfrac{3}{70\sqrt{7}}$$
In a journey of 50 km, in half an hour with 18 carriages
30 = $$\dfrac{3}{70\sqrt{7}}*\dfrac{50\sqrt{50}*18}{\sqrt{X}}$$
Thus, $$\sqrt{X} = \dfrac{9*\sqrt{50}}{7*\sqrt{7}}$$
Thus, X = 11.8
Hence, option B is the correct answer.