Problems On Trains All Competence Aptitude

To find the speed of the train, we'll first calculate the total distance it covers, then use the formula for speed.

Given:
- Length of the train = 50 meters
- Length of the platform = 100 meters
- Time taken to pass the platform = 10 seconds

Total distance covered by the train = Length of train + Length of platform

Total distance = 50 meters + 100 meters = 150 meters

Now, we'll use the formula for speed:

\[ \text{Speed} = \dfrac{\text{Total distance}}{\text{Time taken}} \]

\[ \text{Speed} = \dfrac{150 \, \text{m}}{10 \, \text{s}} \]

Now, let's convert the speed from meters per second to kilometers per hour:

\[ \text{Speed} = \dfrac{150 \, \text{m}}{10 \, \text{s}} \times \dfrac{3600 \, \text{s}}{1000 \, \text{m}} \]

\[ \text{Speed} = \dfrac{150 \times 3600}{10 \times 1000} \, \text{km/hr} \]

\[ \text{Speed} = \dfrac{540000}{10000} \, \text{km/hr} \]

\[ \text{Speed} = 54 \, \text{km/hr} \]

So, the speed of the train is \( 54 \, \text{km/hr} \).

Therefore, the correct answer is:

\( 54 \, \text{km/hr} \).

To find the time it takes for the train to cross the bridge, we need to consider the length of both the train and the bridge, and then use the formula for speed.

Given:
- Length of the train = 270 meters
- Speed of the train = 36 km/h
- Length of the bridge = 180 meters

First, let's convert the speed of the train from kilometers per hour to meters per second, as the length of the train and the bridge are given in meters.

\[ \text{Speed} = 36 \times \dfrac{1000}{3600} = 10 \, \text{m/s} \]

Now, let's find the total distance the train needs to cover, which is the sum of the length of the train and the length of the bridge.

\[ \text{Total distance} = \text{Length of train} + \text{Length of bridge} \]\[ \text{Total distance} = 270 \, \text{m} + 180 \, \text{m} = 450 \, \text{m} \]

Now, we'll use the formula for speed:

\[ \text{Speed} = \dfrac{\text{Total distance}}{\text{Time taken}} \]

Rearranging this equation to solve for time:

\[ \text{Time taken} = \dfrac{\text{Total distance}}{\text{Speed}} \]

\[ \text{Time taken} = \dfrac{450 \, \text{m}}{10 \, \text{m/s}} \]

\[ \text{Time taken} = 45 \, \text{seconds} \]

So, it will take 45 seconds for the train to cross the bridge.

Therefore, the correct answer is:

45 sec.

To find the speed of the train, we need to consider the time it takes to cross both platforms.

Given:
- Length of the first platform = 162 meters
- Time taken to cross the first platform = 18 seconds
- Length of the second platform = 120 meters
- Time taken to cross the second platform = 15 seconds

Let's denote:
- Length of the train = \( L \) meters (which we need to find)
- Speed of the train = \( S \) m/s

When the train crosses a platform, it covers the length of the platform and its own length. So, the total distance covered by the train is the sum of the length of the train and the length of the platform.

For the first platform:\[ L + 162 \, \text{m} = S \times 18 \, \text{s} \]

For the second platform:\[ L + 120 \, \text{m} = S \times 15 \, \text{s} \]

We can solve this system of equations to find \( L \) and \( S \).

First, let's solve the first equation for \( L \):\[ L = 18S - 162 \]

Now, let's substitute this expression for \( L \) into the second equation:\[ 18S - 162 + 120 = 15S \]\[ 18S - 42 = 15S \]\[ 3S = 42 \]\[ S = 14 \]

Now, let's find \( L \) using the value we found for \( S \):\[ L = 18S - 162 \]\[ L = 18 \times 14 - 162 \]\[ L = 252 - 162 \]\[ L = 90 \]

So, the speed of the train is \( S = 14 \) m/s and the length of the train is \( L = 90 \) meters.

Now, let's convert the speed from m/s to km/hr:\[ S = 14 \times \dfrac{3600}{1000} \]\[ S = 50.4 \, \text{km/hr} \]

So, the speed of the train is \( 50.4 \) km/hr.

Therefore, the correct answer is:

\( 50.4 \) km/hr.

To find the length of the train, we'll first determine the speed of the train using the information provided, and then use this speed to find the length of the train.

Let's denote:
- Length of the train as \( L \) meters
- Speed of the train as \( v \) m/s

Given:
- Length of the first platform = 162 meters
- Time taken to pass the first platform = 18 seconds
- Length of the second platform = 120 meters
- Time taken to pass the second platform = 15 seconds

When the train passes a platform, it covers the length of the platform and its own length. So, the total distance covered by the train is the sum of the length of the train and the length of the platform.

Using the formula for speed \( \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \), we can express the speed of the train for each platform:

For the first platform:\[ v = \dfrac{162 + L}{18} \]

For the second platform:\[ v = \dfrac{120 + L}{15} \]

Since the speed of the train is constant, we can equate the two expressions for speed:

\[ \dfrac{162 + L}{18} = \dfrac{120 + L}{15} \]

Now, let's solve this equation for \( L \), the length of the train:

\[ 15(162 + L) = 18(120 + L) \]\[ 2430 + 15L = 2160 + 18L \]\[ 18L - 15L = 2430 - 2160 \]\[ 3L = 270 \]\[ L = 90 \]

So, the length of the train is \( L = 90 \) meters.

Therefore, the correct answer is \( 90 \) meters.

To find the time it takes for the train to cross the platform, we first need to calculate the total distance the train covers, which includes the length of both the train and the platform.

Given:
- Length of the train = 120 meters
- Speed of the train = 90 km/h
- Length of the platform = 230 meters

First, let's convert the speed of the train from kilometers per hour to meters per second:\[ \text{Speed} = 90 \times \dfrac{1000}{3600} = 25 \, \text{m/s} \]

Now, let's find the total distance the train needs to cover:\[ \text{Total distance} = \text{Length of train} + \text{Length of platform} \]\[ \text{Total distance} = 120 \, \text{m} + 230 \, \text{m} = 350 \, \text{m} \]

Now, we'll use the formula for speed:\[ \text{Speed} = \dfrac{\text{Total distance}}{\text{Time taken}} \]

Rearranging this equation to solve for time:\[ \text{Time taken} = \dfrac{\text{Total distance}}{\text{Speed}} \]\[ \text{Time taken} = \dfrac{350 \, \text{m}}{25 \, \text{m/s}} \]

Now, let's calculate the time:\[ \text{Time taken} = \dfrac{350}{25} = 14 \, \text{seconds} \]

So, it will take \( 14 \) seconds for the train to cross the platform.

Therefore, the correct answer is \( 14 \) seconds.

To find the length of the tunnel, we need to first calculate the time it takes for the train to cross the tunnel, and then use this time to find the length of the tunnel.

Given:
- Length of the train = 800 meters
- Speed of the train = 78 km/hr
- Time taken to cross the tunnel = 1 minute = 60 seconds

First, let's convert the speed of the train from kilometers per hour to meters per second:\[ \text{Speed} = 78 \times \dfrac{1000}{3600} = 21.67 \, \text{m/s} \]

Now, let's find the distance the train travels in 1 minute:\[ \text{Distance} = \text{Speed} \times \text{Time} \]\[ \text{Distance} = 21.67 \times 60 = 1300 \, \text{meters} \]

The total distance the train covers is the sum of the length of the train and the length of the tunnel. Since the train covers the length of the tunnel as well during this time, we can subtract the length of the train from the total distance to find the length of the tunnel:\[ \text{Length of tunnel} = \text{Total distance} - \text{Length of train} \]\[ \text{Length of tunnel} = 1300 - 800 = 500 \, \text{meters} \]

So, the length of the tunnel is \( 500 \) meters.

Therefore, the correct answer is \( 500 \) meters.

Let's denote the length of the train (and the platform) as \( L \) meters.

Given:
- Speed of the train = 90 km/hr
- Time taken to cross the platform = 1 minute = 60 seconds

First, let's convert the speed of the train from kilometers per hour to meters per second:\[ \text{Speed} = 90 \times \dfrac{1000}{3600} = 25 \, \text{m/s} \]

Now, we'll use the formula for speed:\[ \text{Speed} = \dfrac{\text{Total distance}}{\text{Time taken}} \]

Rearranging this equation to solve for total distance:\[ \text{Total distance} = \text{Speed} \times \text{Time taken} \]\[ \text{Total distance} = 25 \times 60 = 1500 \, \text{meters} \]

The total distance the train covers is the sum of the length of the train and the length of the platform:\[ \text{Total distance} = \text{Length of train} + \text{Length of platform} = 2L \]

Now, we have:\[ 2L = 1500 \]\[ L = \dfrac{1500}{2} = 750 \, \text{meters} \]

So, the length of the train is \( 750 \) meters.

Therefore, the correct answer is \( 750 \) meters.

Let's first find the relative speed between the train and the man.

Given:
- Speed of the train = 36 km/hr
- Speed of the man = 9 km/hr

Relative speed between the train and the man is the difference in their speeds since they are moving in opposite directions:
Relative speed = Speed of the train - Speed of the man

\[ \text{Relative speed} = 36 \, \text{km/hr} - 9 \, \text{km/hr} = 27 \, \text{km/hr} \]

Now, we need to convert this relative speed from kilometers per hour to meters per second as the length of the train is given in meters and we want the answer in seconds.\[ \text{Relative speed} = 27 \times \dfrac{1000}{3600} = 7.5 \, \text{m/s} \]

Now, we can find the time taken by the train to pass the man using the formula:\[ \text{Time} = \dfrac{\text{Distance}}{\text{Speed}} \]

The distance here is the length of the train, which is \( 150 \) meters.

\[ \text{Time} = \dfrac{150 \, \text{m}}{7.5 \, \text{m/s}} \]\[ \text{Time} = 20 \, \text{seconds} \]

So, the time taken by the train to pass the man is \( 20 \) seconds.

Therefore, the correct answer is \( \textbf{20 seconds} \).

To find the length of the train, we first need to convert the speed of the train from kilometers per hour to meters per second since the time taken to cross the pole is given in seconds.

Given:
- Speed of the train = 36 km/hr
- Time taken to cross the pole = 25 seconds

First, let's convert the speed of the train from kilometers per hour to meters per second:\[ \text{Speed} = 36 \times \dfrac{1000}{3600} = 10 \, \text{m/s} \]

Now, using the formula:\[ \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \]

We can rearrange this formula to solve for the distance (length of the train):\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:\[ \text{Distance} = 10 \times 25 = 250 \, \text{meters} \]

So, the length of the train is \( \textbf{250 meters} \).

Therefore, the correct answer is \( \textbf{250 meters} \).

To find the length of the train, we need to consider the time it takes for the train to pass the pole and the platform.

Given:
- Time taken to pass the pole = 20 seconds
- Time taken to pass the platform = 45 seconds
- Length of the platform = 250 meters

Let's denote the length of the train as \( L \) meters.

When the train passes the pole, it covers only its own length. When it passes the platform, it covers both its own length and the length of the platform.

Using the formula for speed \( \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \), we can express the speed of the train for each scenario:

1. Passing the pole:\[ \text{Speed} = \dfrac{L}{20} \]

2. Passing the platform:\[ \text{Speed} = \dfrac{L + 250}{45} \]

Since the speed of the train is constant, we can equate the two expressions for speed:

\[ \dfrac{L}{20} = \dfrac{L + 250}{45} \]

Now, let's solve this equation for \( L \), the length of the train:

\[ 45L = 20(L + 250) \]\[ 45L = 20L + 5000 \]\[ 45L - 20L = 5000 \]\[ 25L = 5000 \]\[ L = \dfrac{5000}{25} \]\[ L = 200 \]

So, the length of the train is \( L = 200 \) meters.

Therefore, the correct answer is \( 200 \) meters.