SSC Sample Paper Mock Test-18 SSC CGL Tear-II Paper-1

A train passes a standing man in 3 s and a platform 105 m long in 8 s. Find the speed of the train

A) 75.6 km/h

B) 70.80 km/h

C) 65.54 km/h

D) 45.25 km/h

Correct Answer: A

Solution :

Let the length of the train be x metres and its speed be y km/h i.e., \[\left( \frac{5y}{18} \right)\text{m/s}\]

Then, \[\frac{x}{\left( \frac{5y}{18} \right)}=3\]\[\Rightarrow \]\[18x=15y\]\[\Rightarrow \]\[6x=5y\]

Also, \[\frac{(x+105)}{\left( \frac{5y}{18} \right)}=8\]\[\Rightarrow \]\[18\,\,(x+105)=40\,\,y\]

\[\Rightarrow \]\[9\,\,(x+105)=20y\]\[\Rightarrow \]\[20y-9x=945\]

\[\Rightarrow \]\[24x-9x=945\]

\[\Rightarrow \] \[15x=945\]\[\Rightarrow \]\[x=63\]

\[\therefore \] \[5y=(6\times 63)\]\[\Rightarrow \]\[y=\frac{6\times 63}{5}=\frac{378}{5}=75.6\]

Hence, the length of the train is 63 m and its speed is 75.6 km/h.