Problems on Trains

A train passes a station platform in $36 \mathrm{seconds}$ and a man standing on the platform in $20 \mathrm{seconds}$. If the speed of the train in $54 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$, what is the length of the platform?

A fort had provision of food for $150$men for $45$days. After $10$days, $25$men left the fort. The number of days for which the remaining food will last, is:

Two trains of length of $250 \mathrm{m}$ and $200 \mathrm{m}$ are running in the same direction, if the trains cross each other in $45 \mathrm{seconds}$ and the speed of the first train is $27 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$, find speed of the second train.

Two trains, $125 \mathrm{metres}$ and $115 \mathrm{metres}$ in length, are running towards each other on parallel lines, one at the rate of $33 \mathrm{kmph}$ and the other at $39 \mathrm{kmph}$. How much time (in $\sec$) will they take to pass each other from the moment they meet?

Two friends sitting in two different trains whose are parallel to each other start running and ratio of their speed is $3:7$. The time taken to cross a person standing on platform are in ratio $4:5$. If sum of their length is $940 m$ then find the ratio of the sum of length of train to difference between the length of two both trains?

Seema left Chandigarh for Delhi in his car at $6:45 AM$. On his way to Delhi at $8:00 AM$ she met Shreya, who was heading towards Chandigarh. If Shreya reaches Chandigarh at $10:00 AM$, then find the ratio of Seema and Shreya's car speed.

Two trains Shatabdi express and Bhagirathi crosses each other in $40 \mathrm{s}$ when running in opposite direction. Bhagirathi crossed a pole in $8 \mathrm{s}$. If the ration of speed of both the train are in ration $2:5$, then what are the ration of their length.

Two trains of length$500 \mathrm{m}$ and $800 \mathrm{m}$ passes each other with constant speed in opposite directions. The time gap between the drives in both the trains passing each other and the first driver guard pair passing each other is $40\sec$. Then find the ratio of the time of the first driver guard passing each other to second driver guard pass each other after passing the first driver guard.

Two trains $340 \mathrm{m}$ and $560 \mathrm{m}$ long-running in opposite direction cross another train each other in $21.6$ second. If the ratio of the speed of the first and second train is $3:2$, then the second train crossed by the first train in how many second if both trains run in the same direction find the ratio between and the first train.

The train from Jammu Tawi to Baramulla passes through the Pir Pranjal Railway Tunnel which is $9.90 \mathrm{km}$ while the total distance to be covered between Banihal and Quazigund between which the Pir Pranjal Railway Tunnel is situated, is $11.22 \mathrm{km}$. The train’s length is $330 \mathrm{m}$. It is found that the train’s speed outside the tunnel is $10\%$ more than inside the tunnel, then what should be the speed of the train inside the tunnel if the train takes $11 \min$ $45$ seconds to cross the distance between Banihal and Quazigund?

Mansi estimates and tries to frame a mathematical equation that relates the time taken by a train and its speed. She figures out that the speed of the train while covering $495 km$ can be expressed as twice the time taken by the train to cover the distance plus a factor of $3$. If the expression holds good when it covers $693 km$ as well, then what would be the ratio of the time taken by the train to cover the distance and the speed of the train?

Ayan is travelling by Darjeeling Himalayan Railway’s Toy Train. He sits on the Toy Train from Ghum which is the highest altitude station on the Darjeeling Himalayan Railway’s route to Darjeeling in $3$ hours. While going back Ayan goes from Darjeeling, he reaches Batasia Loop in $3$ hours which is a few kms from Ghum. He finds that he covers a total of $24$ kms in the $6$ hours. Also, he is told by the Driver that the train gains $1 km/hr$ while descending from Ghum to Darjeeling while loses $1 km/hr$ while going from Darjeeling to Ghum. Based on this, how much time would it take for the train to go from Batasia Loop to Ghum?

A Shatabdi express and an express train are going along the same direction with speeds of $100 km/hr$ and $75$ km/hr respectively. The Shatabdi express comes from behind and crosses a man standing in the express train in $54$ seconds. Assuming that the ratio of the Shatabdi train’s length to the express train’s length is $\frac{5}{6}$, then what is the length of the express train?

Train A is travelling at $63 \mathrm{kmph}$ can cross a platform $199.5 \mathrm{m}$ long in $21$ seconds. How much time would train A take to completely cross (from the moment they meet) train B, $287 \mathrm{m}$ long and travelling at $54 \mathrm{kmph}$ in an opposite direction of that in which Train A is travelling? 

If speed of Satabadi and Tejas express is in ratio $6:5$. If Tejas express runs $380 \mathrm{km}$ in $4 \mathrm{hours}$. Then find the speed of Satabadi Express.

The ratio of length of two trains is $7\frac{1}{2}: 6\frac{2}{3}$ and the ratio of their speed is $8\frac{1}{2}: 9\frac{1}{3}$. Find the ratio of time taken by them to cross a pillar.

A train covers the distance between Lucknow and Delhi in $12 \mathrm{minutes}$. The distance between Lucknow and Delhi is $10 \mathrm{km}$. If speed of train is decreased by $5 \mathrm{km}/\mathrm{hr}$, then time taken by train to cover the same distance will be _____?

Tejas express covered two rivers of length $400 \mathrm{m}$ and $200 \mathrm{m}$ in $50 \mathrm{second}$ and $30 \mathrm{second}$ respectively. Then find the time taken by it to cover $252 \mathrm{km}$.

A train passes a $100 \mathrm{metres}$ long market in $28 \mathrm{second}$ and a boy standing in the market in $20 \mathrm{second}$. The speed of train is _____?

Two trains of speed $60 \mathrm{km}/\mathrm{hr}$ and $70 \mathrm{km}/\mathrm{hr}$ are running in same direction in the parallel lines. Faster train crosses the slower train in $72 \sec$. If the length of the slower train is $120 \mathrm{m}$, find the length of the faster train.