SSC Sample Paper Mock Test-8 SSC CGL Tear-II Paper-1

A train overtakes two persons walking in the same direction in which the train is going. These person are walking at the rate of 2 km/h and 4 km/h and the train passes them completely in 9 s and 10 s, respectively. The length of the train is

A)         72 m

B) 54 m

C) 50 m

D) 45 m

Correct Answer: C

Solution :

Let the length of the train be x km and its speed be y km/h

Speed of the train relative to first man

\[=(y-2)km/h\]

Speed of the train relative to second man

\[=(y-4)km/h\]

\[\therefore \] \[\frac{x}{(y-2)}=\frac{9}{(60\times 60)}\]

and \[\frac{x}{(y-4)}=\frac{10}{(60\times 60)}\]

\[\Rightarrow \] \[y-2=400x\] and \[y-4=360x\]

\[\Rightarrow \]\[400x+2=360x+4\]

\[\Rightarrow \] \[40x=2\]

\[\Rightarrow \] \[x=\frac{1}{20}\text{km}\]

\[=\left( \frac{1}{20}\times 1000 \right)\text{m}=50\,\,\text{m}\]

\[\therefore \] Length of the train\[=50\,\,\text{m}\]