GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 16:42 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  A train crosses a bridge of length 500 m in 40 seconds and a lamp post

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58340
A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

2
16 00:00

Difficulty:   55% (hard)

Question Stats: 63% (02:06) correct 38% (02:16) wrong based on 220 sessions

HideShow timer Statistics

A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

_________________
Director  P
Joined: 21 May 2013
Posts: 636
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of train=LT
Speed of train=VT

Time taken =(Length of train +Length of Bridge)/Speed of Train
40=(LT+500)VT
And, LT/VT=15
Put LT/VT=15 in the first equation,
15+500/VT=40
VT=20
Using value of VT=20, LT=300M
Manager  Joined: 08 Sep 2012
Posts: 59
Location: India
Concentration: Social Entrepreneurship, General Management
WE: Engineering (Investment Banking)
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Length of train = L
Speed of train = S

(L+500) = S*40
L = S*15 => S = (L / 15)

=> L+500 = (L / 15) * 40
=> L = 300m

Option E
_________________
+1 Kudos if you liked my post! Thank you!
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

3
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of Train = L

Case-1: Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time = (500+L)/40

Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15

But Since speed has to be same in both cases so

(500+L)/40 = (L)/15

i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager  Joined: 10 Jun 2015
Posts: 111
A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

let the length of the train is L
L/15 = (L+500)/40
solving, L=300
Manager  B
Joined: 14 Mar 2014
Posts: 142
GMAT 1: 710 Q50 V34 Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

IMO: E

Speed = $$\frac{Distance}{time}$$

Let Length of train be $$L_T$$
Let Length of Bridge be $$L_B$$
Speed of train be S

While crossing Lamp post
S = $$\frac{L_T}{15}$$
$$L_T$$ = 15S --(i)

While crossing Bridge
s = $$\frac{L_T + L_B}{40}$$
40s = $$L_T$$+$$L_B$$
40s = 15s+500 (from eq--(i) & given length of bridge = 500)
s= 20

Sub in eq-(i) we get $$L_T$$ = 300
_________________
I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯ Retired Moderator Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

You have two concepts covered in this topic: a train which crosses a stationary object with (1) and without (2) length:

Crossing a stationary object with length (bridge = 500m):

r * t = Length of Train + Length of object ->> Where r = spdeed and t = time

In this question we get: 40r = 500 + Length of Bridge

then crossing a stationary object without length/with negligible length:

r*t = Length of train

So we have 15r = Length of Train ->> plug in above to get:

40r = 500 + 15r
25r = 500
r = 20

Plug in r = 20 in 15r = Length of train to get Length = 300.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8048
Location: United States (CA)
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

We can let x = the length of the train in metres. To cross the 500-m bridge in 40 seconds, the head of the train must enter at one end of the bridge and the tail of the train must exit from the other end of the bridge. Therefore, in 40 seconds, the train actually travels the length of the bridge plus the train’s body length. In other words, the train travels (500 + x) metres in 40 seconds. If we let r be the speed of the train, we have:

500 + x = 40r

Since there are two unknowns, we need another equation in order to solve for x. We will use the fact that the train crosses a lamp post on the bridge in 15 seconds. This means that after the head of the train first crosses the lamp post, it takes 15 seconds for the train’s tail to cross the lamp post too. In other words, the train travels a distance equal to its body length in 15 seconds. So, we have:

x = 15r

Substitute x = 15r in the first equation and we have:

500 + 15r = 40r

500 = 25r

20 = r

So, we know the speed of the train is 20 m/s and its body length is x = 15r = 15(20) = 300 metres.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

GMATinsight wrote:
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of Train = L

Case-1: Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time = (500+L)/40

Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15

But Since speed has to be same in both cases so

(500+L)/40 = (L)/15

i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300

hey GMATinsight
not familiar with such type of questions. are there specific formulas for such concepts ? thanks!
Manager  G
Joined: 14 Jun 2018
Posts: 219
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
dave13 wrote:
GMATinsight wrote:
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of Train = L

Case-1: Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time = (500+L)/40

Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15

But Since speed has to be same in both cases so

(500+L)/40 = (L)/15

i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300

hey GMATinsight
not familiar with such type of questions. are there specific formulas for such concepts ? thanks!

hey , this should help with train related concepts https://www.hitbullseye.com/Quant/Probl ... Trains.php
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

Solution

Given:
• A train crosses a bridge of length 500 m in 40 seconds.
• A train crosses a lamp post on the bridge in 15 seconds.

To find:
• Length of the train in metres.

Approach and Working

Let the length of train is ‘t’ metres and speed of train is ‘s’ m/s.
• Therefore, we can frame two equations.

A train crosses a bridge of length 500 m in 40 seconds.
• In this case, train covers its length as well as the distance of bridge.
o Hence, t+500= 40*s------(1)

A train crosses a lamp post on the bridge in 15 seconds.

• In this case, train covers only its length.
o Hence, t= 15*s

• Substituting this value of t in equation 1, we get:
o 15s +500 = 40s
o 25s=500
o s= 20 m/s
 Hence, t= 15*20= 300 m

Correct answer: Option E
_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

1
dave13 wrote:
GMATinsight wrote:
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of Train = L

Case-1: Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time = (500+L)/40

Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15

But Since speed has to be same in both cases so

(500+L)/40 = (L)/15

i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300

hey GMATinsight
not familiar with such type of questions. are there specific formulas for such concepts ? thanks!

dave13

Search for Time speed and distance questions and you would find plenty of such questions

There are not many formulas only a few concepts like Relative speed, River and boat problems etc.
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  B
Joined: 07 Jul 2018
Posts: 44
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post  [#permalink]

Show Tags

GMATinsight wrote:
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of Train = L

Case-1: Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time = (500+L)/40

Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15

But Since speed has to be same in both cases so

(500+L)/40 = (L)/15

i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300

I'm not able to understand the basic thing. Can you please explain why we add length of train and bridge length but in case of lamp post, why do we take train length? Shouldn't it be lamp post's length? Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post   [#permalink] 04 Nov 2018, 05:30
Display posts from previous: Sort by

A train crosses a bridge of length 500 m in 40 seconds and a lamp post

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  