Answer: Option C
$$\eqalign{
& {\text{Speed}} = \left( {78 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{{65}}{3}} \,{\text{m/sec}} \cr
& {\text{Time = }}\,{\text{1}}\,{\text{minute = 60}}\,{\text{second}}. \cr
& {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{tunnel}}\,{\text{be}}\,x\,{\text{metres}}. \cr
& {\text{Then}},\, {\frac{{800 + x}}{{60}}} = \frac{{65}}{3} \cr
& \Rightarrow 3\left( {800 + x} \right) = 3900 \cr
& \Rightarrow x = 500 \cr} $$