Question : Two trains 100 metres and 95 metres long, respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. The speeds of the two trains are:
Option 1: 44 km/hr, 22 km/hr
Option 2: 52 km/hr, 26 km/hr
Option 3: 36 km/hr, 18 km/hr
Option 4: 40 km/hr, 20 km/hr
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Correct Answer: 52 km/hr, 26 km/hr
Solution : Let the speed of the first train be $x$ km/hr and the speed of the second train is $y$ km/hr. Time = $\frac{\text{Total distance}}{{\text{Relative speed in same/Opposite direction}}}$ In the same direction, ⇒ $27=\frac{100+95}{(x-y)×\frac{5}{18}}$ ⇒ $27=\frac{195×18}{5(x-y)}$ ⇒ $x-y=26$ ----------------(i) In the opposite direction, ⇒ $9=\frac{100+95}{(x+y)×\frac{5}{18}}$ ⇒ $9=\frac{195×18}{5(x+y)}$ ⇒ $x+y=78$ ------------------(ii) Solving equation (i) and (ii), we get, $x=52,$ and $y=26$ Hence, the correct answer is 52 km/hr and 26 km/hr.
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Question : Two trains 150 m and 120 m long respectively moving from opposite directions cross each other in 10 seconds. If the speed of the second train is 43.2 km/hr, then the speed of the first train is:
Option 1: 54 km/hr
Option 2: 50 km/hr
Option 3: 52 km/hr
Option 4: 51 km/hr
Question : Two trains are moving in the same direction at the speed of 44 km/hr and 70 km/hr. The time taken by a faster train to cross a man sitting in the slower train is 72 seconds. What will be the length of the faster train?
Option 1: 520 metres
Option 2: 620 metres
Option 3: 450 metres
Option 4: 500 metres
Question : Two boats are travelling at the speed of 36 km/hr and 54 km/hr respectively towards each other. What will be the distance between the two boats one second before they collide?
Option 1: 40 metres
Option 2: 35 metres
Option 3: 25 metres
Option 4: 15 metres
Question : A 900-metre-long train crosses a 1200 metres long platform completely in 70 seconds. What is the speed of the train?
Option 1: 117 km/hr
Option 2: 108 km/hr
Option 3: 99 km/hr
Option 4: 90 km/hr
Question : Train P crosses train Q completely in 45 seconds while running in opposite directions. The lengths of train P and train Q are 1200 metres and 1500 metres respectively. The speed of train Q is 144 km/hr. In how much time can train P to cross an 1800 metres long platform?
Option 1: 180 seconds
Option 2: 175 seconds
Option 3: 120 seconds
Option 4: 150 seconds
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