## Problems on Trains Questions - 1

A train is running at 63 km/h, then its speed per second is ?
• 60 m/sec
• 17.5 m/sec
• 22.5 m/sec
• 15 m/sec
• 7.5 m/sec
Explanation

Speed of the train is 63 Km/hr, then speed per second

=> 63 $\displaystyle \times \frac{5}{18}$ = 17.5 meters/sec.

Workspace
Speed of a train is 22.5 m/s, then its speed per hour is ?
• 90 km/hr
• 72 km/hr
• 81 km/hr
• 99 km/hr
• 108 km/hr
Explanation

Speed of the train per second is 22.5 meters/sec.

Speed of the train per hour => 22.5 $\displaystyle \times \frac{18}{5}$ = 81 km/hr.

Workspace
Moving at 54 km/h, a train crosses a signal pole in 15 seconds, then length of the train is ?
• 250 meters
• 200 meters
• 240 meters
• 225 meters
• 245 meters
Explanation

Time taken by a train to cross a pole = Time taken to cross its own length.

Length of the train = 54 $\displaystyle \times \frac{5}{18} \times 15$ = 225 meters.

Workspace
A train, moving at 72 km/hr crosses a platform 250 meter long in 30 seconds, then length of the train is ?
• 350 meters
• 400 meters
• 275 meters
• 425 meters
• 375 meters
Explanation

Rule: While crossing a platform a train covers the length of the platform and its own length.

Distance covered by the train in 30 seconds, moving at 72 Km/hr is 72 $\displaystyle \times \frac{5}{18} \times 30$ = 600 meters.

Length of the train = Distance covered â€“ length of the platform = 600 m â€“ 250 m = 350 meters.

Workspace
Moving at 60 km/hr, a train passes a bridge in 45 seconds, what is the length of the train, if length of the bridge and train is equal.
• 450 meters
• 750 meters
• 425 meters
• 400 meters
• 375 meters
Explanation

Rule: While crossing a bridge a train covers the length of bridge and its own length.

Distance covered by the train in 45 seconds at 60 Km/hr

=> 60 $\displaystyle \times \frac{5}{18} \times 45$ = 750 meters.

Length of the trains = $\displaystyle \frac{750}{2}$ = 375 meters [ as both length of the train and bridge is equal ]

Workspace
A train whose length is 200 meters crosses a platform of 250 meters length in 20 seconds, then speed of the trains is ?
• 90 km/hr
• 81 km/hr
• 72 km/hr
• 63 km/hr
• 54 km/hr
Explanation

Speed per second = $\displaystyle \frac{\text{Length of the train} + \text{Length of the platform}}{\text{Time}}$

Speed per second = $\displaystyle \frac{200 \ \text{m} \ + \ 250 \ \text{m}}{20 \ \text{sec}} \ = \ \frac{450}{20}$ = 22.5 meters/sec.

Speed of the train per hour = 22.5 $\displaystyle \times \frac{18}{5}$ = 81 km/hr.

Workspace
A train crosses a platform in 30 seconds and a signal pole in 10 seconds, then ratio of the lengths of platform and train respectively is ?
• 3 : 1
• 3 : 2
• 4 : 1
• 4 : 3
• 2 : 1
Explanation

While crossing a platform a train covers the length of the platform and its own length.

 Time taken to cross the platform = 30 seconds (-)Time taken to cross the signal pole = 10 seconds [train length] To cross only platform length = 20 seconds

Ratio of time taken to cross plat form to train = 20 sec : 10 sec or 2 : 1

Workspace
A train is of 200 meter length, crosses a 400 meter platform in 24 seconds, then time taken to cross a bridge of 800 meter length is ?
• 48 sec
• 42 sec
• 50 sec
• 40 sec
• 45 sec
Explanation

Distance covered in 24 seconds = length of the train + length of the platform.

Speed of the train per second => $\displaystyle \frac{200 + 400}{24} = \frac{600}{24}$ = 25 m/s.

Speed of the train = 25 $\displaystyle \times \frac{18}{5}$ = 90 km/hr.

Time taken to cross a bridge of 800 meters => $\displaystyle \frac{\text{bridge length} + \text{train length}}{\text{speed}}$

Time taken to cross the bridge => $\displaystyle \frac{800 \ \text{m} \ + 200 \ \text{m}}{25 \ \text{m/s}} = \frac{1000}{25}$ = 40 seconds.

Workspace
Time taken by a train of 1 km long travelling at 1 km/minute, to pass through a tunnel, which is also 1 km long is ?
• 3 minutes
• 1 minute
• 2 minutes
• 4 minutes
• 5 minutes
Explanation

As the speed of the train is 1 Km/min, and length of the train is 1 Km.

Length of the tunnel = 1 Km, distance to be covered = 1 + 1 = 2 Km.

Therefore the train takes 2 min to pass through the tunnel.

Workspace
A train was started at 7:00 AM at certain speed and reached its destination at 11:00 AM, while returning back the speed of the train was increased by 25% and the train was started at 12 noon. At what time would it return to the starting point ?
• 3 : 12 PM
• 3 :00 PM
• 2 : 30 PM
• 2 : 48 PM
• 3 : 15 PM
Explanation

Time taken = 4 Hrs [From 7:00 am to 11:00 am].

If speed increases by R% then time reduces by = $\displaystyle \frac{\text{R}}{100 + \text{R}} \times 100$

Then time reduces by = $\displaystyle \frac{25}{125} \times 100$ = 20%.

4 hours = 240 minutes = 20% of 240 = 48 minutes.

4 hours â€“ 48 minutes = 3 hours and 12 minutes.

The train reaches at 12:00 Noon + 3 hrs 12 min = 3:12 PM.

Workspace

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## Problems on Trains Important Formulas

If a train is moving at A km/h then its speed per second is

A $\displaystyle \times \frac{5}{18}$ meters second.

If a train is moving at B meters per second then its speed per hour is

B $\displaystyle \times \frac{18}{5}$ km/hour.

Time taken to cross pole/tree/standing person etc.. is time taken to cross its own length of the train.

While crossing a platform/Bridge/Tunnel the train covers the length of the platform/Bridge/Tunnel and its own length.

### Relative speed:

If two trains are moving at x km/hr and y km/hr respectively, then relative speed if they are moving in.

Opposite direction = [ x + y ] km/hr

Same direction = [ x â€“ y ] km/hr

Note: Add lengths of the trains in both the cases.

Time: