Question

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction and (ii) in the opposite direction is
1. \(\frac{3}{2}\)
2. \(\frac{{25}}{{11}}\)
3. \(\frac{{11}}{5}\)
4. \(\frac{5}{2}\)

Answer 1

Correct Answer - Option 3 : \(\frac{{11}}{5}\)

Concept:

When trains are moving in same direction relative speed = |v₁ – v₂|

In opposite direction, relative speed = |v₁ + v₂|

Hence, ratio of time when trains move in same direction with time when trains move in opposite direction is

\(\Rightarrow \frac{{{{\rm{t}}_1}}}{{{{\rm{t}}_2}}} = \frac{{\left( {\frac{{{{\rm{l}}_1} + {{\rm{l}}_2}}}{{\left| {{{\rm{u}}_1} - {{\rm{v}}_2}} \right|}}} \right)}}{{\left( {\frac{{{{\rm{l}}_1} + {{\rm{l}}_2}}}{{\left| {{{\rm{v}}_1} + {{\rm{v}}_2}} \right|}}} \right)}} = \frac{{\left| {{{\rm{v}}_1} + {{\rm{v}}_2}} \right|}}{{\left| {{{\rm{v}}_1} - {{\rm{v}}_2}} \right|}}\) 

Where,

l₁ + l₂ = Sum of lengths of trains which is same as distance covered by trains to cross each other.

Calculation:

\(\Rightarrow \frac{{{t_1}}}{{{t_2}}} = \frac{{80 + 30}}{{80 - 30}} = \frac{{110}}{{50}}\) 

\(\therefore \frac{{{t_1}}}{{{t_2}}} = \frac{{11}}{5}\)