A train 120 m long passes a telegraph post in 6 seconds. Find the speed of the train.
Answer: D
A telegraph post has no length, so the train covers only its own 120 m.
\[ v = \frac{120}{6} = 20 \text{ m/s} \]
\[ 20 \times \frac{18}{5} = 72 \text{ km/hr} \]
The factor \( \tfrac{18}{5} \) converts m/s to km/hr.
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Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
Answer: B
Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.
Passing the driver of the other train means covering only the slower train's own length.
\[ \text{relative speed} = 45 + 30 = 75 \text{ km/hr} = 75 \times \frac{5}{18} = \frac{125}{6} \text{ m/s} \]
\[ t = \frac{500 \times 6}{125} = 24 \text{ seconds} \]
Passing the whole train would need 1000 m and take 48 seconds - which is why that value is on the list.
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Two trains A and B are moving in the same direction. A has speed of 8 km/h and B has speed of 13 km/h. What is relative speed of B with respect to A?
Answer: B
Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ 13 - 8 = 5 \text{ km/hr} \]
Because they travel the same way, only the excess of B's speed over A's brings them together. In opposite directions the answer would be their sum, 21 km/hr - which is why that value is offered.
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A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec 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.
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A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Answer: B
A tree is a point, so the first crossing gives the speed.
\[ v = \frac{1200}{120} = 10 \text{ m/s} \]
\[ t = \frac{1200 + 700}{10} = 190 \text{ seconds} \]
Timing only the platform's 700 m would give 70 seconds; the train's own length is part of the crossing.
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A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Answer: B
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
\[ 54 \text{ km/hr} = 15 \text{ m/s} \]
The man is a point, so that crossing gives the train's length:
\[ L = 15 \times 20 = 300 \text{ m} \]
The platform crossing covers train plus platform:
\[ 15 \times 36 = 540 \quad\Longrightarrow\quad P = 540 - 300 = 240 \text{ m} \]
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Two trains are moving in the same direction at 50 km/hr and 30 km/hr. The faster train crosses a man in the slower train in 18 seconds. Find the length of faster train.
Answer: B
Crossing a man in the other train covers only the faster train's length.
\[ \text{relative speed} = 50 - 30 = 20 \text{ km/hr} = 20 \times \frac{5}{18} = \frac{50}{9} \text{ m/s} \]
\[ L = \frac{50}{9} \times 18 = 100 \text{ m} \]
The slower train's length is irrelevant, because the reference point is a single person, not the whole train.
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A train travels a certain distance by taking 3 stops of 20 minutes each. Considering the period of stoppage, the overall speed of the train comes to 40 kmph; while without consideration of stoppage, it is 60 kmph. How much distance must the train have travelled ?
Answer: B
Three stops of 20 minutes cost exactly one hour, so the journey with stops takes an hour longer.
\[ \frac{D}{40} - \frac{D}{60} = 1 \]
\[ D\left(\frac{3 - 2}{120}\right) = 1 \quad\Longrightarrow\quad D = 120 \text{ km} \]
Checking: 3 hours with stops against 2 hours of pure running.
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Two trains 140 metres and 120 metres are running in the same direction with speeds 40 kmph and 60 kmph respectively. In what time will the faster train pass the slower one?
Answer: C
Total distance = addition of length of the two trains = 140 + 120 = 260 metres
As the two trains are travelling in the same direction, their relative speed is:
v = | v1 - v2 | = | 40 - 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min
t = 260/ 1000*3
t = 0.78 minutes
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Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Answer: C
Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ \text{relative speed} = 60 + 90 = 150 \text{ km/hr} = 150 \times \frac{5}{18} = \frac{125}{3} \text{ m/s} \]
\[ \text{total length} = 1100 + 900 = 2000 \text{ m} \]
\[ t = \frac{2000 \times 3}{125} = 48 \text{ seconds} \]
The lengths are given in kilometres and must be converted to metres first.
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