In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?
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Solution
Speed = m/sec = 40 meter/sec.
Time taken = sec = 2.5 sec.
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
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Solution
Speed of the train relative to man = 125/10 m/sec = 12.5 m/sec.
⇒ [12.5 × 18/5] km/hr = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x – 5) = 45 km/hr.
x – 5 = 45
x = 50 km/hr.
Two trains, one from A to B and the other from B to A, start simultaneously. After they meet the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
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Solution
Let us name the train as A and B. then,
(A’s speed) : (B’s speed) =
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
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Solution
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m /sec.
∴ = 3x
⇔ 24x = 200
⇔ x =
So, speed of the faster train = km/hr = 60 km/hr.
A train X speeding with 120 kmph crosses another train Y, running in the same direction, in 2 minutes. If the lengths of the train X and Y be 100 m and 200 m respectively, what is the speed of train Y?
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Solution
Let the speed of train Y be x km/hr.
Speed of X relative to Y = (120 – x) km/hr
=
∴ = 120 ⇔ 5400 = 120 (600-5x) ⇔ x = 111.
Train A, starts from Merrut at 4 pm arrives Ghaziabad at 5 pm. Other train B, starts from Ghaziabad at 4 pm arrives Merrut at 5:30 pm. When will both trains meet?
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Solution
Let distance between Merrut and Ghaziabad = 'x' km
Time taken by 'A' to cover 'x' km = 1 hr
Time taken by 'B' to cover 'x' km = hr
∵ Speed of A = = x km/hr
Speed of B = = km/hr
Let both trains meet after 'y' hours.
Then xy + = x
y + = 1
y = hrs
y = ×60 = 36 minutes
So they will meet 4:36 PM
A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train?
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Solution
Length of the train l = 150 m
Speed of the man = 2 km/hr
Relative speed = total distance/time = m/s = × = 180 km/hr
Relative Speed = Speed of train - Speed of man (As both are moving in the same direction)
⇒ 180 = speed of train – 2
⇒ speed of train = 180 + 2 = 182 km/hr
A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
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Solution
Speed = 45 km/hr = m/s
= m/s
Total distance = length of the train + length of the platform
= 360 + 140 = 500 meter
Time taken to cross the platform = = 40 seconds
A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is?
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Solution
Speed of the train = 54 km/hr = m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15 × 20 = 300 m
Let the length of the platform = L
Time taken to cross the platform =
⇒ = 36
⇒ 300 + L = 15 × 36 = 540
⇒ L = 540 – 300 = 240 meter
A train passes a post and a 264 m long platform in 8 seconds and 20 seconds respectively. What is the speed of the train?
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Solution
Let x is the length of the train and v is the speed
Time taken to move the post = 8 seconds
⇒ = 8
⇒ x = 8v --- (1)
Time taken to cross the platform 264 m long = 20 s
= 20
⇒ x + 264 = 20v ---(2)
Substituting equation 1 in equation 2, we get
8v + 264 = 20v
⇒ v = = 22 m/s
km/hr = 79.2 km/hr