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Two trains running in opposite directions cross a man standing on the platform 54s and 34s respectively and they cross each other in 46 s . Find the ratio of their speeds. ?
Let the speeds of two trains be x and y, respectively . ∴ Length of 1st train = 54x Length of the 2nd train = 34y According to the question. (54x + 34y) / (x + y) = 46⇒ 54x + 34y = 46x + 46y ⇒ 27x + 17y = 23x + 23y ⇒ 4x = 6y ⇒ x/y = 3/2
∴ x : y = 3 : 2
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15 Qs. 45 Marks 15 Mins
Given:
Two train crosses the man in 25 seconds and 32 seconds respectively.
Two trains running in opposite direction and they crosses each other in 30 second
When two running object moving in opposite direction their relative speed = Sum of their speed
Concept Used:
Calculation:
Let, the speed of the 1st train be x m/sec and that of the 2nd train is y m/sec
When a train crosses a standing man it cross its won length
1st train cross the man in 25 second
⇒ Length of 1st train is 25x meter
2nd train cross the man in 32 seconds
⇒ Length of the 2nd train is 32y meter
Relative speed of two trains is (x + y) m/sec
In 30 seconds they cross each other
⇒ In 30 seconds the cross 30(x + y) meter
Accordingly,
30(x + y) = 25x + 32y
⇒ 30x + 30y = 25x + 32y
⇒ 30x - 25x = 32y - 30y
⇒ 5x = 2y
⇒ x/y = 2/5
⇒ x : y = 2 : 5
∴ The ratio of speed of two trains is 2 : 5.
Let's discuss the concepts related to Speed Time and Distance and Relative Speed. Explore more from Quantitative Aptitude here. Learn now!
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Here we will learn about the concept of two trains passes in the opposite direction.
When two train passes a moving object (having some length) in the opposite direction
Let length of faster train be l meters and length of slower train be m meters
Let the speed of faster train be x km/hr
Relative speed = (x + y) km/hr.
Then, time taken by the faster
train to pass the slower train = (l
+ m) meters/(x + y) km/hr
Now we will learn to calculate when two trains running on parallel tracks (having some length) in the opposite direction.
Solved examples when two trains passes (having some length) in the opposite direction:
1. Two trains of length 150 m and 170 m respectively are running at the speed of 40 km/hr and 32 km/hr on parallel tracks in opposite directions. In what time will they cross each other?
Solution:
Relative speed of train = (40 + 32) km/hr
= 72 km/hr
= 72 × 5/18 m/sec
= 20 m/sec
Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains
= (150 + 170)/20 sec
= 320/20 sec
= 16 sec
Therefore, the two trains crossed each other in 16 seconds.
2. Two trains 163 m and 187 m long are running on parallel tracks in the opposite directions with a speed of 47 km/hr and 43 km/hr in. How long will it take to cross each other?
Solution:
Relative speed of train = (47 + 43) km/hr
= 90 km/hr
= 90 × 5/18 m/sec
= 25 m/sec
Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains
= (163 + 187)/25 sec
= 350/25 sec
= 14 sec
Therefore, the two trains crossed each other in 14 seconds.
Speed of Train
Relationship between Speed, Distance and Time
Conversion of Units of Speed
Problems on Calculating Speed
Problems on Calculating Distance
Problems on Calculating Time
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Train Passes a Moving Object in the Opposite Direction
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Train Passes through a Bridge
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Two Trains Passes in the Opposite Direction
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