Speed, Time and Distance
 A train overtakes two person walking at 2 km per hr. and 4 km per hr. respectively and
passes completely them in 9 sec. and 10 sec. respectively. What is the length of the train?

 65 metres
 60 metres
 55 metres
 50 metres

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Let the length of the train be x km and its speed y km per hr.
Case I : When it passes the man walking at 2 km per hr. in the same direction
Relative speed of train = (y – 2) km per hr.∴ x = 9 seconds y − 2 = 9 = 1 hour ...(i) 3600 400
Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
Relative speed of train= (y – 4) km per hr.∴ x = 10 sec. y − 4 ⇒ x = 10 hrs. y − 4 3600 ⇒ x = 1 hrs. ...(ii) y − 4 360
On dividing equation (i) by (ii),
we havey − 4 = 1/400 = 360 = 9 y − 2 1/360 400 10
⇒ 10y – 40 = 9y – 18
⇒ 10y – 9y = 40 – 18
⇒ y = 22 km per hr.
∴ From equaton (i), we have
⇒x = 1 22 − 2 400 ⇒ x = 1 km 20 = 1000 = 50 metres. 20 Correct Option: D
Let the length of the train be x km and its speed y km per hr.
Case I : When it passes the man walking at 2 km per hr. in the same direction
Relative speed of train = (y – 2) km per hr.∴ x = 9 seconds y − 2 = 9 = 1 hour ...(i) 3600 400
Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
Relative speed of train= (y – 4) km per hr.∴ x = 10 sec. y − 4 ⇒ x = 10 hrs. y − 4 3600 ⇒ x = 1 hrs. ...(ii) y − 4 360
On dividing equation (i) by (ii),
we havey − 4 = 1/400 = 360 = 9 y − 2 1/360 400 10
⇒ 10y – 40 = 9y – 18
⇒ 10y – 9y = 40 – 18
⇒ y = 22 km per hr.
∴ From equaton (i), we have
⇒x = 1 22 − 2 400 ⇒ x = 1 km 20 = 1000 = 50 metres. 20
 A train travelling at the rate of 60 km per hr, while inside a tunnel, meets another train of half its length travelling at 90 km per hr.
Find the length of the tunnel if the first train passes completelyand passes completely in 4 1 seconds. 2 through it in 4 minutes 37 1 seconds. 2

 5 km
 3.5 km
 4.5 km
 6 km

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Trains are running in opposite direction.
∴ Relative speed of the two trains
= 90 + 60 = 150 km per hr.Distance travelled in 4 1 seconds 2
with speed of 150 km per hr.= 150 × 5 m per sec. 18 = 150 × 5 × 9 18 2 = 375 metres 2
Let the length of the first train be x metres.Then the length of the second train be x metres 2 ∴ x + x = 375 2 2 ⇒ 3x = 375 2 2
⇒ 3x = 375
⇒ x = 125 metres
Hence, the length of the first
train = 125 metres
Speed of the first train = 60 km per hr.= 60 × 5 m per sec. 18 = 50 m per sec. 3
Time taken by the first train to cross the tunnel = 4 minutesand 37 1 sec. 2 = 240 + 75 sec. = 480 + 75 2 2 = 555 sec. 2 Speed of first train = 50 m per sec. 3 ∴ Distance covered by it in 555 sec. 2 = 50 × 555 = 4625 metres 3 2
Hence, length of tunnel
= 4625 – 125 = 4500 metres
= 4.5 kmCorrect Option: C
Trains are running in opposite direction.
∴ Relative speed of the two trains
= 90 + 60 = 150 km per hr.Distance travelled in 4 1 seconds 2
with speed of 150 km per hr.= 150 × 5 m per sec. 18 = 150 × 5 × 9 18 2 = 375 metres 2
Let the length of the first train be x metres.Then the length of the second train be x metres 2 ∴ x + x = 375 2 2 ⇒ 3x = 375 2 2
⇒ 3x = 375
⇒ x = 125 metres
Hence, the length of the first
train = 125 metres
Speed of the first train = 60 km per hr.= 60 × 5 m per sec. 18 = 50 m per sec. 3
Time taken by the first train to cross the tunnel = 4 minutesand 37 1 sec. 2 = 240 + 75 sec. = 480 + 75 2 2 = 555 sec. 2 Speed of first train = 50 m per sec. 3 ∴ Distance covered by it in 555 sec. 2 = 50 × 555 = 4625 metres 3 2
Hence, length of tunnel
= 4625 – 125 = 4500 metres
= 4.5 km
 Two trains 200 metres and 175 metres long are running on parallel lines.
They take 7 1 seconds.when running in opposite directions 2
to pass each other. Find their speeds in km per hour.and 37 1 seconds when running in the same direction 2

 118 kmph ; 75 kmph
 108 kmph ; 72 kmph
 120 kmph ; 75 kmph
 125 kmph ; 80 kmph

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Let the speed of the train be x metre per sec. and y metre per sec. respectively.
Sum of the length of the trains = 200 + 175 = 375 metres
Case : I
When the trains are moving in opposite directions
Relative speed = (x + y) m per sec.
In this case the time taken by the trains to cross each other= 375 sec. x + y ∴ 375 = 15 x + y 2
⇒ x + y = 50 ...(i)
Case : II
When the trains are moving in the same direction.
Relative speed = (x – y) m per sec.
In this case, the time taken by the trains to cross each other= 375 sec. x − y ∴ 375 = 75 x − y 2
⇒ x – y = 10 ...(ii)
Now, x + y = 50x – y = 10 _________ 2x = 60
⇒ x = 30
Putting this value in equation (i),
we have
y = 50 – 30 = 20
∴ Speed of trains = 30 m per sec.= 30 × 18 = 108 km per hr. 5 and 20 m per sec. = 20 × 18 = 72 km per hr. 5 Correct Option: B
Let the speed of the train be x metre per sec. and y metre per sec. respectively.
Sum of the length of the trains = 200 + 175 = 375 metres
Case : I
When the trains are moving in opposite directions
Relative speed = (x + y) m per sec.
In this case the time taken by the trains to cross each other= 375 sec. x + y ∴ 375 = 15 x + y 2
⇒ x + y = 50 ...(i)
Case : II
When the trains are moving in the same direction.
Relative speed = (x – y) m per sec.
In this case, the time taken by the trains to cross each other= 375 sec. x − y ∴ 375 = 75 x − y 2
⇒ x – y = 10 ...(ii)
Now, x + y = 50x – y = 10 _________ 2x = 60
⇒ x = 30
Putting this value in equation (i),
we have
y = 50 – 30 = 20
∴ Speed of trains = 30 m per sec.= 30 × 18 = 108 km per hr. 5 and 20 m per sec. = 20 × 18 = 72 km per hr. 5
 A train running at 25 km per hour take 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at the rate of 5 km per hr. in the same direction. Find the length of the platform.

 25 metres
 20 metres
 24 metres
 28 metres

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Let the length of train be x metres and the length of platform be y metres.
Speed of the train = 25 × 5 m/sec 18 = 125 m per sec. 18
Time taken by train to pass the platform= (x + y) × 18 sec. 125 ∴ (x + y) × 18 = 18 125
or, x + y = 125 ...(i)
Speed of train relative to man = (25 + 5) km per hr.= 30 × 5 m per sec. 18 = 25 m per sec. 3
Time taken by the train to pass the man= x × 3 sec. 25 = 3x sec. 25 ∴ 3x = 12 25 ⇒ x = 25 × 12 = 100 metres 3
Putting x = 100 in equation (i),
we get, y = 25 metres.
∴ Length of train = 100 metres
and length of the platform = 25 metres.Correct Option: A
Let the length of train be x metres and the length of platform be y metres.
Speed of the train = 25 × 5 m/sec 18 = 125 m per sec. 18
Time taken by train to pass the platform= (x + y) × 18 sec. 125 ∴ (x + y) × 18 = 18 125
or, x + y = 125 ...(i)
Speed of train relative to man = (25 + 5) km per hr.= 30 × 5 m per sec. 18 = 25 m per sec. 3
Time taken by the train to pass the man= x × 3 sec. 25 = 3x sec. 25 ∴ 3x = 12 25 ⇒ x = 25 × 12 = 100 metres 3
Putting x = 100 in equation (i),
we get, y = 25 metres.
∴ Length of train = 100 metres
and length of the platform = 25 metres.
 Two places A and B are 162 kms apart. A train leaves A for B and at the same time another train leaves B for A. The two trains meet at the end of 6 hours. If the train travelling from A to B travels 8 km per hr. faster than the other, find the speed of the faster train.

 16.5 kmph
 16 kmph
 17 kmph
 17.5 kmph

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Both trains meet after 6 hours.
∴ The relative speed of two trains= 162 = 27 km per hr. 6
The speed of the slower train starting from B= 27 − 8 = 19 =9 1 km per hr. 2 2 2
∴ The speed of the faster train= 9 1 + 8 = 17 1 km per hr. 2 2 Correct Option: D
Both trains meet after 6 hours.
∴ The relative speed of two trains= 162 = 27 km per hr. 6
The speed of the slower train starting from B= 27 − 8 = 19 =9 1 km per hr. 2 2 2
∴ The speed of the faster train= 9 1 + 8 = 17 1 km per hr. 2 2