$\begin{array}{1 1}(A)\;78\;km\;h^{-1}\\(B)\;18km\;h^{-1} \\(C)\;67\;km\;h^{-1} \\(D)\;45\;km\;h^{-1}\end{array} $

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Let s kilometer be the total distance of the journey .

Suppose the time taken in hours to cover first one-third and the last one third of the journey be$t_1,t_2 $ and $t_2$ respectively . Then

$t_1= \large\frac{s/3}{10}$

$t_2= \large\frac{s/3}{20}$

$t_3= \large\frac{s/3}{10}$

Total time of journey $t=t_1+t_2+t_3$

$\qquad = \large\frac{s}{(3)(10)} +\frac{s}{(3)(20)}+\frac{s}{(3)(60)}$

$\qquad= \large\frac{s}{18} $$h$

Average velocity $= \large\frac{\text{total distance in km}}{\text{total time in h }}$

$\qquad= \large\frac{s}{(s/18)}$$=18 km\;h^{-1}$

Hence B is the correct answer.

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