Question

Two trains start simultaneously from Kanpur and Agra towards each other with speeds of 70 km/hr and 90 km/hr respectively. When they met each other it was observed that one of them had covered 350 km more than the other. Find distance between Kanpur and Agra.
A) 2400 km
B) 2550 km
C) 2700 km
D) 2800 km

Answer 1

Hint: Here both trains are running towards each other with their respective speed. Both trains will meet each other after a time of say t hour. As speed $s = \dfrac{d}{t}$ so, distance travel by train is given by $d = s \cdot t$. As one train has travelled 350 km more distance than the second train, so ${d_2} = {d_1} + 350$. Put ${d_1} = {s_1} \cdot t$ and ${d_2} = {s_2} \cdot t$ in ${d_2} = {d_1} + 350$ equation and calculate time t. Total distance between two stations will be $d = {d_1} + {d_2}$. By using value of s1 and s2, calculate d1 and d2 by using ${d_1} = {s_1} \cdot t$ and ${d_2} = {s_2} \cdot t$. After this use $d = {d_1} + {d_2}$ to obtain distance between two stations.

Complete step-by-step answer:
Here, given that two trains are starting simultaneously from Kanpur and Agra towards each other with speeds of 70 km/hr and 90 km/hr respectively.
Let’s say train-1 is starting from station Kanpur with a speed of 70 km/hr and train-2 is starting from station Agra with a speed of 90 km/hr.
So, speed ${s_1} = 70km/hr$ and ${s_2} = 90km/hr$.
After a time of t hour, both trains are meeting at a point.
Total distance between Kanpur and Agra is d. Let’s say the distance travelled by train-1 from Kanpur to the meeting point is $d_1$ and by train-2 from Agra to the meeting point is $d_2$. Above things are illustrated in the diagram below. So, we can say that $d = {d_1} + {d_2}$.

As we know that speed $s = \dfrac{d}{t}$ , so distance $d = s \cdot t$.
Here for train-1 distance travelled in time t is given by ${d_1} = {s_1} \cdot t$.
So, putting value of speed of train-1 ${s_1} = 70km/hr$ , ${d_1} = 70 \cdot t$.
And for train-2 distance travelled in time t is given by ${d_2} = {s_2} \cdot t$.
So, putting value of speed of train-2 ${s_2} = 90km/hr$ , ${d_2} = 90 \cdot t$.
At the meeting point it was observed that one of the trains had covered 350 km more distance than the other train. Here the speed of train-2 is more as compared to train-1, so train-2 must have covered more distance than train-1.
So, we can write that distance travelled by train-2 = distance travelled by train-1 + 350
So, ${d_2} = {d_1} + 350$
Putting ${d_1} = 70 \cdot t$ and ${d_2} = 90 \cdot t$ in the above equation.
$90 \cdot t = 70 \cdot t + 350$
Taking ala terms of t on one side of equation,
$90 \cdot t - 70 \cdot t = 350$.
Take t common in left side terms of equation, $(90 - 70) \cdot t = 350$
So, $20 \cdot t = 350$
Simplifying, $t = \dfrac{{350}}{{20}}$
So, $t = 17.5hr$.
So, distance travelled by train-1 in time t hour is, ${d_1} = 70 \cdot t$. Put $t = 17.5hr$
So, ${d_1} = 70 \cdot 17.5$
So, ${d_1} = 1225km$
And, distance travelled by train-2 in time t hour is, ${d_2} = 90 \cdot t$. Put $t = 17.5hr$
So, ${d_2} = 90 \cdot 17.5$
So, ${d_2} = 1575km$.
Total distance between Kanpur and Agra is $d = {d_1} + {d_2}$.
Putting ${d_1} = 1225km$ and ${d_2} = 1575km$,
$d = 1225 + 1775$
$d = 2800km$
So, Distance between Kanpur and Agra is 2800km.

Option (D) is the correct answer.

Note: While solving the problems regarding trains, take care of the following points. If both trains are travelling in the same direction then their relative speed will be different speeds of both trains, while for opposite direction travel relative speed will be the sum of speeds of both trains. If it is given that the train of length l traveling at speed s crosses a stationary man/pole in time t, then time t is calculated by using $t = \dfrac{l}{s}$ formula. If a train of length l traveling at speed s crosses a platform/bridge of length m in time t, then time is calculated by using $t = \dfrac{{l + m}}{s}$ formula.