A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Answer: A
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
\[ 45 \text{ km/hr} = 12.5 \text{ m/s} \]
\[ t = \frac{360 + 140}{12.5} = \frac{500}{12.5} = 40 \text{ seconds} \]
Please log in or register to report this question.
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Answer: B
The man walks toward the train, so the speeds add.
\[ \text{relative speed} = 60 + 6 = 66 \text{ kmph} = 66 \times \frac{5}{18} = \frac{55}{3} \text{ m/s} \]
A man is a point, so only the train's own length is covered:
\[ t = \frac{110 \times 3}{55} = 6 \text{ seconds} \]
Had he walked the same way as the train, the relative speed would be 54 kmph and the answer about 7.3 seconds.
Please log in or register to report this question.
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Answer: B
Two trains that meet and then take \( t_{1} \) and \( t_{2} \) to finish have speeds in the ratio
\[ \frac{v_{1}}{v_{2}} = \sqrt{\frac{t_{2}}{t_{1}}} \]
\[ = \sqrt{\frac{16}{9}} = \frac{4}{3} \quad\Longrightarrow\quad 4 : 3 \]
The square root is essential; taking the times directly would give 9 : 16, which is offered as the last option and is also the wrong way round.
Please log in or register to report this question.
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Answer: B
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
\[ 63 \text{ km/hr} = 63 \times \frac{5}{18} = 17.5 \text{ m/s} \]
A tree is a point, so the train covers only its own length:
\[ t = \frac{280}{17.5} = 16 \text{ seconds} \]
The conversion is where the answer is decided: at 17.5 m/s the 280 m takes exactly 16 seconds, not 15.
Please log in or register to report this question.
A train passes a stationary pole in 8 seconds. The train also passes a 200 m long bridge in 28 seconds. What is the length and the speed of the train?
Answer: C
The pole crossing covers only the train:
\[ L = 8v \]
The bridge crossing covers the train plus 200 m:
\[ L + 200 = 28v \quad\Longrightarrow\quad 8v + 200 = 28v \]
\[ 20v = 200 \quad\Longrightarrow\quad v = 10 \text{ m/s} \]
\[ L = 80 \text{ m} \]
Only one option gives a pair consistent with both crossings.
Please log in or register to report this question.
Jammu Express is 1.2 km long and is running along the Kerala express at speed of 80km/hr. Kerala express is 2/3rd the length of Jammu express and runs at 60 km/hr. How much time will it take for Jammu express to overtake the Kerala express?
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.
Please log in or register to report this question.
A train running at 60 km/hr overtakes a man walking at 6 km/hr in the same direction and passes him in 12 seconds. What is the length of the train ?
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.
\[L = 15 \times 12 = 180 \text{ m}\]
Please log in or register to report this question.
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Answer: B
Let the train's speed be \( v \) kmph. Passing a walking person covers the train's own length at the relative speed.
\[ L = (v - 2) \times \frac{5}{18} \times 9 = (v - 4) \times \frac{5}{18} \times 10 \]
\[ 9(v - 2) = 10(v - 4) \quad\Longrightarrow\quad 9v - 18 = 10v - 40 \]
\[ v = 22 \text{ kmph} \]
\[ L = 20 \times \frac{5}{18} \times 9 = 50 \text{ m} \]
Please log in or register to report this question.
A boy sitting in a train counts the electricity poles along the line as he passes them. If they are 40 m apart and the speed of the train is 48 km/h, how many poles does he pass per minute ?
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
Please log in or register to report this question.
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
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.
Please log in or register to report this question.
