Problems on Trains Questions and Answers

Answer: B

Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.

\[ \text{Kerala express length} = \frac{2}{3} \times 1200 = 800 \text{ m} \]

\[ \text{relative speed} = 80 - 60 = 20 \text{ km/hr} = 20 \times \frac{5}{18} = \frac{50}{9} \text{ m/s} \]

To overtake, the Jammu express must cover both lengths:

\[ t = \frac{1200 + 800}{50/9} = \frac{2000 \times 9}{50} = 360 \text{ s} = 6 \text{ minutes} \]

Overtaking always needs the sum of the lengths, even though the speeds subtract.

Answer: B

Correct answer: 180 m

Since both move the same way, the speeds subtract.

\[60 - 6 = 54 \text{ km/hr} = 54 \times \frac{5}{18} = 15 \text{ m/s}\]

Passing a man means covering only the train’s length.

\[L = 15 \times 12 = 180 \text{ m}\]

Answer: B

Let the train's speed be \( v \) kmph. Passing a walking person covers the train's own length at the relative speed.

\[ L = (v - 2) \times \frac{5}{18} \times 9 = (v - 4) \times \frac{5}{18} \times 10 \]

\[ 9(v - 2) = 10(v - 4) \quad\Longrightarrow\quad 9v - 18 = 10v - 40 \]

\[ v = 22 \text{ kmph} \]

\[ L = 20 \times \frac{5}{18} \times 9 = 50 \text{ m} \]

Answer: C

Speed of train = 48 km/h = (48 * 1000)/60 m/minute
= 800 m/minute
Thus we have to find the number of poles situated along a distance of 800 with each pole at a distance of 40 m from each other.

|--------40 m-------|--------40 m ---------|
Consider a distance of 80 m. There are 3 poles situated along this distance as shown.
Thus number of poles = 80/40 + 1 = 2 + 1 = 3
Similarly along a distance of 900 m, number of poles situated
= 800/40 + 1 = 21

Answer: D

The post crossing covers the train alone; the bridge crossing adds 264 m.

\[ L = 8v, \qquad L + 264 = 20v \]

\[ 12v = 264 \quad\Longrightarrow\quad v = 22 \text{ m/s} \]

\[ 22 \times \frac{18}{5} = 79.2 \text{ km/hr} \]

The train works out at 176 m long, though the question asks only for the speed.

Answer: D

\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]

\[ 90 \text{ km/hr} = 25 \text{ m/s} \]

In one minute the train covers

\[ 25 \times 60 = 1500 \text{ m} \]

That is the train plus the platform, and the two are equal:

\[ 2L = 1500 \quad\Longrightarrow\quad L = 750 \text{ metres} \]

Answer: B

The man runs the same way, so the train closes on him at the difference of the speeds and covers only its own length.

\[ \text{relative speed} = \frac{125}{10} = 12.5 \text{ m/s} = 12.5 \times \frac{18}{5} = 45 \text{ km/hr} \]

\[ v_{\text{train}} = 45 + 5 = 50 \text{ km/hr} \]

The man's speed is added back because it had been subtracted to give the relative speed.

Answer: B

Using the formula, speed=distance/time

Speed of truck = 550/60 m/s

Speed of train= 33000/(45*60) m/s

Ratio of speed of truck to train= (550/60 ) / [33000/(45*60)]

=3:4

Answer: B

Let the speeds be \( a \) and \( b \) m/s. Crossing a man gives each length:

\[ L_{1} = 27a, \qquad L_{2} = 17b \]

Running opposite ways they cross in 23 seconds, covering both lengths at \( a + b \):

\[ \frac{27a + 17b}{a + b} = 23 \]

\[ 27a + 17b = 23a + 23b \quad\Longrightarrow\quad 4a = 6b \]

\[ \frac{a}{b} = \frac{3}{2} \quad\Longrightarrow\quad 3 : 2 \]

Neither actual speed is needed - the lengths cancel out into the ratio.

Answer: D

Passing a man sitting in the slower train means covering only the fast train's own length, at the difference of the speeds.

\[ \text{relative speed} = 40 - 20 = 20 \text{ km/hr} = 20 \times \frac{5}{18} = \frac{50}{9} \text{ m/s} \]

\[ L = \frac{50}{9} \times 5 = \frac{250}{9} = 27\tfrac{7}{9} \text{ m} \]

The slower train's length never enters, because the reference point is one seated person.