Express 25 mps in kmph?
Answer: C
\[ 1 \text{ m/s} = \frac{18}{5} \text{ km/hr} \]
\[ 25 \times \frac{18}{5} = 90 \text{ kmph} \]
Going from m/s to kmph the number always grows, since a metre per second is a little over 3.6 kmph - so any option below 25 can be discarded at once.
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A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Answer: C
Crossing a telegraph post means covering the train's own length.
\[ v = \frac{240}{16} = 15 \text{ m/s} \]
\[ 15 \times \frac{18}{5} = 54 \text{ kmph} \]
The conversion factor \( \tfrac{18}{5} \) turns m/s into kmph; using \( \tfrac{5}{18} \) by mistake would give 4.17 kmph, far too slow for a train.
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Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Answer: D
Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ \text{relative speed} = 42 + 30 = 72 \text{ kmph} = 20 \text{ m/s} \]
\[ t = \frac{120 + 280}{20} = \frac{400}{20} = 20 \text{ sec} \]
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A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:
Answer: C
Let \( a \) be the hours on foot and \( b \) the hours on the bicycle.
\[ a + b = 9, \qquad 4a + 9b = 61 \]
Substituting \( b = 9 - a \):
\[ 4a + 81 - 9a = 61 \quad\Longrightarrow\quad -5a = -20 \quad\Longrightarrow\quad a = 4 \text{ h} \]
\[ \text{distance on foot} = 4 \times 4 = 16 \text{ km} \]
Setting up the unknowns as times rather than distances is what makes the second equation linear; the question then asks for a distance, so one more multiplication is needed at the end.
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Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Answer: B
Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
\[ \text{relative speed} = 54 + 72 = 126 \text{ kmph} = 35 \text{ m/s} \]
To cross completely, the gap and both lengths must be covered:
\[ 100 + 100 + 200 = 400 \text{ m} \]
\[ t = \frac{400}{35} = \frac{80}{7} \text{ sec} \]
Meeting takes only \( \tfrac{20}{7} \) seconds; crossing takes four times as long.
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A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
Answer: B
Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
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Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Answer: C
The slower car takes one hour longer over the same distance.
\[ \frac{d}{60} - \frac{d}{64} = 1 \]
\[ d\left(\frac{64 - 60}{3840}\right) = 1 \quad\Longrightarrow\quad \frac{4d}{3840} = 1 \]
\[ d = 960 \text{ km} \]
The unit matters: the answer is in kilometres, since the speeds were given in kmph.
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Find the area of the square field if a train 800 metres long passes the field with a speed of 120 kmph in one minute.
Answer: A
In one minute the train travels
\[ 120 \text{ kmph} = \frac{120000}{60} = 2000 \text{ m/min} \]
To pass the field, the train must cover the field's length plus its own length:
\[ \text{side} = 2000 - 800 = 1200 \text{ m} = 1.2 \text{ km} \]
\[ \text{area} = (1.2)^{2} = 1.44 \text{ sq. km} \]
Forgetting to subtract the train's own length would give a 2 km side and an area of 4 sq. km - exactly the second option.
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Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
Answer: A
Trains in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ 1 \text{ kmph} = \frac{5}{18} \text{ m/s} \]
Crossing a man in the other train covers only the faster train's length.
\[ \text{relative speed} = 72 - 36 = 36 \text{ kmph} = 10 \text{ m/s} \]
\[ L = 10 \times 27 = 270 \text{ m} \]
The slower train's own length is irrelevant, since the reference point is a single person.
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Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
Answer: B
Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
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