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A train crosses a man standing on a platform 150 meters long in 10 sec

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Bunuel
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A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   07 Feb 2021, 14:29
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A train crosses a man standing on a platform 150 meters long in 10 seconds and crosses the platform completely in 22 seconds. What is the length of the train?

A. 90 meters
B. 100 meters
C. 125 meters
D. 150 meters
E. 180 meters
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C
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manan subba
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Re: A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   07 Feb 2021, 21:23
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speed of train = 150/10-> 15 mts/sec

(length of train+length of platform)= 15* 22 sec=330

hence length of train=330-150=180
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A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   Updated on: 08 Feb 2024, 04:34
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\(S = \frac{D}{T} = Constant\)

Let \(x\) be the length of the train.

\(\frac{x}{10}=\frac{150+x}{22}\)

\(x=\dfrac{150 \times 10}{12}=5 \times 25 = 125\) m

Ans C

Originally posted by meanup on 07 Feb 2021, 22:45.
Last edited by meanup on 08 Feb 2024, 04:34, edited 1 time in total.
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somyamehta777
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Re: A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   Updated on: 13 Feb 2021, 03:36
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Bunuel
I think the answer should be 125.
Let x be the length of the train.

Speed of train = x / 10 -> When the person is crossed, the length of the train is crossed.
Speed of train = (x+150) / 22 -> When platform is crossed both length of platform and train is crossed.

Equating we get,

x/10 = (x+150)/12

12x = 1500
x=125

Please give a kudos if anyone agree with the explanation provided above.

Originally posted by somyamehta777 on 09 Feb 2021, 13:06.
Last edited by somyamehta777 on 13 Feb 2021, 03:36, edited 3 times in total.
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Re: A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   09 Feb 2021, 14:07
Train, of length x crosses a man or a pt on the platform in 10 seconds
ie x mtr in 10 sec or speed = x/10 m/s

Now it entirely crosses the platform in 22 secs
ie it crosses a length of 150 m plus the length of train in 22 sec
Or we can say 150+x mtr in 22 sec

Equating both we know it took 12 secs to cross 150 mtr
So its speed is 150 mtr in 12 secs or 12.5 m/s

Putting it in eq 1
We get x = 125 mtr

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stne
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Re: A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   17 Feb 2021, 08:07
Bunuel wrote:
A train crosses a man standing on a platform 150 meters long in 10 seconds and crosses the platform completely in 22 seconds. What is the length of the train?

A. 90 meters
B. 100 meters
C. 120 meters
D. 150 meters
E. 180 meters


Bunuel

Answer should be 125m , Here's why:

When crossing the man :\(\frac{t}{s}=10\) where t= length of train and s is speed of train (i)

When crossing the platform : \(\frac{t +150}{s}=22\) (ii)

Putting \(t= 10s\) in (ii)

we get \(s= \frac{25}{2}\)

Hence \(t= 10*\frac{25}{2}=125m\)

Hope it's clear.
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Re: A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   02 Feb 2024, 05:40
Let the length of train, length of platform, and speed of train be L1, L2, x respectively.

L1+L2/X = 22

L1+150 = 22X

L1/X= 10 ( GIVEN)

L1=10X


10X+150=22X
X= 12.5 m/s

Length of train /12.5=10
Length of train = 125m.
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Re: A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   02 Feb 2024, 10:03
10v=d
22v=d+150

22/10=1+150/d
150/d=12/10
=>d=1500/12=125m
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A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink] New post   03 Feb 2024, 14:42
x/10 = (x+150)/22
22x = 10(x+150)
22x = 10x + 1500
12x = 1500
x = 125
Therefore, the length of the train is 125 meters.
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A train crosses a man standing on a platform 150 meters long in 10 sec [#permalink]
03 Feb 2024, 14:42
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