# Problems on Train

## Problems On Trains

 Question 1 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
 A 9 B 10 C 10.8 D 9.6
Question 1 Explanation:
\begin{align} & {\text{Relative}}\, {\text{speed}} = \left( {60 + 40} \right)\, {\text{km/hr}} \cr & = \left( {100 \times \frac{5}{{18}}} \right)\, {\text{m/sec}} \cr & = \left( {\frac{{250}}{9}} \right)\, {\text{m/sec}}. \cr & {\text{Distance}}\, {\text{covered}}\, {\text{in}}\, {\text{crossing}}\, {\text{each}}\, {\text{other}} \cr & = \left( {140 + 160} \right)m = 300\, m \cr & {\text{Required}}\, {\text{time}} \cr & = \left( {300 \times \frac{9}{{250}}} \right)\, {\text{sec}} \cr & = \frac{{54}}{5}\, {\text{sec}} \cr & = 10.8\, {\text{sec}} \cr\end{align}
 Question 2 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A 100 m long train is going at a speed of 60 km/hr. It will cross a 140 m long railway bridge in-
 A 7.2 sec B 14.4 sec C 3.6 sec D 21.6 sec
Question 2 Explanation:
\begin{align} & {\text{Speed }} \cr & {\text{ = }}\left( {60 \times \frac{5}{{18}}} \right){\text{m/sec}} \cr & {\text{ = }}\frac{{50}}{3}{\text{ m/sec}} \cr & {\text{Total distance covered}} \cr & {\text{ = (100 + 140) m = 240 m}} \cr & \therefore {\text{Required time}} \cr & {\text{ = }}\left( {240 \times \frac{3}{{50}}} \right){\text{sec}} \cr & {\text{ = }}\frac{{72}}{5}{\text{sec}} \cr & {\text{ = 14}}{\text{.4 sec}} \cr\end{align}
 Question 3 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Two trains, A ans B start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet. If train A is moving at 45 km/hr, then the speed of the train B is?
 A 54 km/hr B 60 km/hr C 37.5 km/hr D 64.80 km/hr
Question 3 Explanation:
\begin{align} & {\text{In these type of questions use the given}} \cr & {\text{below formula to save your valuable time}} \cr & \frac{{{{\text{S}}...1}}}{{{{\text{S}}...2}}}{\text{ = }}\sqrt {\frac{{{{\text{T}}...2}}}{{{{\text{T}}...1}}}} {\text{ }} \cr & {\text{Where }}{{\text{S}}...1}{\text{, }}{{\text{S}}...2}{\text{ and }}{{\text{T}}...1}{\text{, }}{{\text{T}}...2}{\text{ are the respective}} \cr & {\text{speeds and times of the objects}} \cr & \Rightarrow \frac{{45}}{{{{\text{S}}...2}}} = \sqrt {3\frac{1}{3} \div 4\frac{4}{5}} \cr & {\text{ = }}{{\text{S}}...2}{\text{ = 45}} \times \frac{6}{5}{\text{ = 54 km/hr}} \cr & \therefore {\text{Required speed = 54 km/hr}} \cr\end{align}
 Question 4 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A train 100 meter long meets a man going in opposite direction at 5 km/h and passes him in 71/5 seconds. What is the speed of the train (in km/hr)?
 A 60 km/h B 45 km/h C 50 km/hr D 55 km/hr
Question 4 Explanation:
\begin{align} & {\text{Relative speed of man \& train}} \cr & {\text{ = }}\frac{{100 \times 5}}{{36}} \times \frac{{18}}{5} \cr & {\text{ = 50km/hr}} \cr & \therefore {\text{speed of train}} \cr & {\text{ = 50}} - {\text{5}} \cr & {\text{ = 45 km/hr}} \cr\end{align}
 Question 5 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
 A 10 a.m. B 10.30 a.m. C 9 a.m. D 11 a.m.
Question 5 Explanation:
\begin{align} & {\text{Suppose}}\, {\text{they}}\, {\text{meet}}\, x\, {\text{hours}}\, {\text{after}}\, {\text{7}}\, {\text{a}}{\text{.m}}. \cr & {\text{Distance}}\, {\text{covered}}\, {\text{by}}\, {\text{A}}\, \cr & {\text{in}}\, x\, {\text{hours = 20x}}\, {\text{km}}{\text{.}} \cr & {\text{Distance}}\, {\text{covered}}\, {\text{by}}\, {\text{B}} \cr & \, {\text{in}}\, \left( {x - 1} \right)\, {\text{hours}} = 25\left( {x - 1} \right)\, km \cr & \therefore 20x + 25\left( {x - 1} \right) = 110 \cr & \Rightarrow 45x = 135 \cr & \Rightarrow x = 3 \cr & {\text{So, }}\, {\text{they}}\, {\text{meet}}\, {\text{at}}\, {\text{10}}\, {\text{a}}{\text{.m}}{\text{.}}\, \cr\end{align}
There are 5 questions to complete.