Last visit was: 18 Nov 2025, 14:11 It is currently 18 Nov 2025, 14:11
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Krunaal
User avatar
Tuck School Moderator
Joined: 15 Feb 2021
Last visit: 17 Nov 2025
Posts: 805
Own Kudos:
850
 [20]
Given Kudos: 251
Status:Under the Square and Compass
Location: India
Schools: Booth '26 Kellogg '26 Johnson '26 Tuck '26 Duke '26 Ross '26 HBS '26 Stanford '26 CBS '26 Stern '26 Kellogg Darden '26 Yale '26 Wharton '26
GMAT Focus 1: 755 Q90 V90 DI82
GPA: 5.78
WE:Marketing (Consulting)
Products:
My Reviews
Schools: Booth '26 Kellogg '26 Johnson '26 Tuck '26 Duke '26 Ross '26 HBS '26 Stanford '26 CBS '26 Stern '26 Kellogg Darden '26 Yale '26 Wharton '26
GMAT Focus 1: 755 Q90 V90 DI82
Posts: 805
Kudos: 850
 [20]
A and B are two points on a straight line. Ram runs from A to B while 04 Oct 2024, 08:46
Kudos
Add Kudos
20
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

60% (02:33) correct 40% (02:49) wrong based on 124 sessions

History

Date
Time
Result
Not Attempted Yet
A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

A. \(2\sqrt{2}\)

B. \(2\)

C. \(\frac{1}{2}\)

D. \(\sqrt{2}\)

E. \(\frac{\sqrt{2}}{2}\)
ShowHide Answer
Official Answer
B
User avatar
shaurya_gmat
User avatar
Joined: 05 Jun 2023
Last visit: 14 May 2025
Posts: 67
Own Kudos:
32
 [1]
Given Kudos: 133
GPA: 3
Products:
My Reviews
Posts: 67
Kudos: 32
 [1]
A and B are two points on a straight line. Ram runs from A to B while 04 Oct 2024, 10:21
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
I ended up with t+4/t+1.. (where t is the time from start to the point ram and rahim cross each other)
I spent some time trying to understand if there was a way to eliminate t completely and reach the ratio but couldn't. I ended up marking 2 as substituting t = 1 results in 2, but I was confused by the root(2) [~1.4] option as well.. the other options I was able to cancel out as you cannot get those values with a t+4 / t+1 ratio ..
Is there a better/alternate way to approach this question ?
User avatar
Krunaal
User avatar
Tuck School Moderator
Joined: 15 Feb 2021
Last visit: 17 Nov 2025
Posts: 805
Own Kudos:
850
 [4]
Given Kudos: 251
Status:Under the Square and Compass
Location: India
Schools: Booth '26 Kellogg '26 Johnson '26 Tuck '26 Duke '26 Ross '26 HBS '26 Stanford '26 CBS '26 Stern '26 Kellogg Darden '26 Yale '26 Wharton '26
GMAT Focus 1: 755 Q90 V90 DI82
GPA: 5.78
WE:Marketing (Consulting)
Products:
My Reviews
Schools: Booth '26 Kellogg '26 Johnson '26 Tuck '26 Duke '26 Ross '26 HBS '26 Stanford '26 CBS '26 Stern '26 Kellogg Darden '26 Yale '26 Wharton '26
GMAT Focus 1: 755 Q90 V90 DI82
Posts: 805
Kudos: 850
 [4]
A and B are two points on a straight line. Ram runs from A to B while 04 Oct 2024, 10:48
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
The direct formula for this is, whenever two entities starting from opposite ends at the same time meet at a common point and the total distance they travelled is D, the ratio of their speeds \(\frac{Sa}{Sb} = \sqrt{\frac{Tb}{Ta}}\), where Tb and Ta is the time taken to reach their destination from the common point. Below is the detailed solution,

Let total distance be D, where D = d1 + d2

When Ram and Rahim meet, Ram covers d1 and Rahim covers d2

Speed of Ram = Sa; Speed of Rahim = Sb

We need to find \(\frac{Sa}{Sb}\)

When Ram and Rahim meet,

\(\frac{d1}{Sa} = \frac{d2}{Sb}\) ...............................(as time is same)

\(\frac{d1}{d2} = \frac{Sa}{Sb}\) .................................(1)

Ram takes 1 minute to cover d2, so \(Sa * 1 = d2\)

Rahim takes 4 minutes to cover d1, so \(Sb * 4 = d1\)

Subs. in (1)

\(\frac{Sb*4}{Sa*1} = \frac{Sa}{Sb}\)

\(4*Sb^2 = Sa^2\)

\(\frac{Sa}{Sb} = \frac{2}{1}\)

Answer B.
User avatar
sarthak1701
User avatar
Joined: 11 Sep 2024
Last visit: 16 Nov 2025
Posts: 110
Own Kudos:
50
Given Kudos: 18
GMAT Focus 1: 575 Q77 V81 DI78
GMAT Focus 1: 575 Q77 V81 DI78
Posts: 110
Kudos: 50
A and B are two points on a straight line. Ram runs from A to B while 05 Oct 2024, 01:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Krunaal
The direct formula for this is, whenever two entities starting from opposite ends at the same time meet at a common point and the total distance they travelled is D, the ratio of their speeds \(\frac{Sa}{Sb} = \sqrt{\frac{Tb}{Ta}}\), where Tb and Ta is the time taken to reach their destination from the common point. Below is the detailed solution,

Let total distance be D, where D = d1 + d2

When Ram and Rahim meet, Ram covers d1 and Rahim covers d2

Speed of Ram = Sa; Speed of Rahim = Sb

We need to find \(\frac{Sa}{Sb}\)

When Ram and Rahim meet,

\(\frac{d1}{Sa} = \frac{d2}{Sb}\) ...............................(as time is same)

\(\frac{d1}{d2} = \frac{Sa}{Sb}\) .................................(1)

Ram takes 1 minute to cover d2, so \(Sa * 1 = d2\)

Rahim takes 4 minutes to cover d1, so \(Sb * 4 = d1\)

Subs. in (1)

\(\frac{Sb*4}{Sa*1} = \frac{Sa}{Sb}\)

\(4*Sb^2 = Sa^2\)

\(\frac{Sa}{Sb} = \frac{2}{1}\)

Answer B.
Show more
Hey could you elaborate why have you taken d2 as distance covered by ram in substitution? His distance initially assumed is d1 right?
User avatar
Purnank
User avatar
Joined: 05 Jan 2024
Last visit: 15 Nov 2025
Posts: 680
Own Kudos:
585
Given Kudos: 166
Location: India
Concentration: General Management, Strategy
GMAT Focus 1: 635 Q88 V76 DI80
Products:
My Reviews
GMAT Focus 1: 635 Q88 V76 DI80
Posts: 680
Kudos: 585
A and B are two points on a straight line. Ram runs from A to B while 05 Oct 2024, 01:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shaurya_gmat
I ended up with t+4/t+1.. (where t is the time from start to the point ram and rahim cross each other)
I spent some time trying to understand if there was a way to eliminate t completely and reach the ratio but couldn't. I ended up marking 2 as substituting t = 1 results in 2, but I was confused by the root(2) [~1.4] option as well.. the other options I was able to cancel out as you cannot get those values with a t+4 / t+1 ratio ..
Is there a better/alternate way to approach this question ?
Show more
you were going correct. Refer to the post for meeting time forumla. https://gmatclub.com/forum/trains-a-and ... l#p3455145

meeting time \( t = \sqrt{4*1} = 2\)

Tram = Time taken by Ram to complete route = t + 1 = 3 min
Trah = Time taken by Rahim to complete route = t + 4 = 6 min

now we know speed is inversely proportional to time,

Therfore, \(\frac{Sram}{Srah}= \frac{Trah}{Tram} = \frac{6}{3} = 2\)

Answer is B.
User avatar
Krunaal
User avatar
Tuck School Moderator
Joined: 15 Feb 2021
Last visit: 17 Nov 2025
Posts: 805
Own Kudos:
850
Given Kudos: 251
Status:Under the Square and Compass
Location: India
Schools: Booth '26 Kellogg '26 Johnson '26 Tuck '26 Duke '26 Ross '26 HBS '26 Stanford '26 CBS '26 Stern '26 Kellogg Darden '26 Yale '26 Wharton '26
GMAT Focus 1: 755 Q90 V90 DI82
GPA: 5.78
WE:Marketing (Consulting)
Products:
My Reviews
Schools: Booth '26 Kellogg '26 Johnson '26 Tuck '26 Duke '26 Ross '26 HBS '26 Stanford '26 CBS '26 Stern '26 Kellogg Darden '26 Yale '26 Wharton '26
GMAT Focus 1: 755 Q90 V90 DI82
Posts: 805
Kudos: 850
A and B are two points on a straight line. Ram runs from A to B while 05 Oct 2024, 01:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sure, after Ram and Rahim meet at a common point, Ram has to cover the distance Rahim had covered from Point B i.e. d2 and Rahim has to cover the distance Ram had covered from Point A i.e. d1, hence the interchange. Hope it is clear.
sarthak1701
Krunaal
The direct formula for this is, whenever two entities starting from opposite ends at the same time meet at a common point and the total distance they travelled is D, the ratio of their speeds \(\frac{Sa}{Sb} = \sqrt{\frac{Tb}{Ta}}\), where Tb and Ta is the time taken to reach their destination from the common point. Below is the detailed solution,

Let total distance be D, where D = d1 + d2

When Ram and Rahim meet, Ram covers d1 and Rahim covers d2

Speed of Ram = Sa; Speed of Rahim = Sb

We need to find \(\frac{Sa}{Sb}\)

When Ram and Rahim meet,

\(\frac{d1}{Sa} = \frac{d2}{Sb}\) ...............................(as time is same)

\(\frac{d1}{d2} = \frac{Sa}{Sb}\) .................................(1)

Ram takes 1 minute to cover d2, so \(Sa * 1 = d2\)

Rahim takes 4 minutes to cover d1, so \(Sb * 4 = d1\)

Subs. in (1)

\(\frac{Sb*4}{Sa*1} = \frac{Sa}{Sb}\)

\(4*Sb^2 = Sa^2\)

\(\frac{Sa}{Sb} = \frac{2}{1}\)

Answer B.
Hey could you elaborate why have you taken d2 as distance covered by ram in substitution? His distance initially assumed is d1 right?
Show more
User avatar
ParthM011
User avatar
Joined: 08 Jun 2024
Last visit: 14 Nov 2025
Posts: 2
Given Kudos: 1
Schools: ISB '27 (S)
Schools: ISB '27 (S)
Posts: 2
Kudos: 0
A and B are two points on a straight line. Ram runs from A to B while 09 Oct 2024, 11:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
d2 is the remaining distance he will be covering, it is denoted as d2 because that is equivalent to the distance that was covered by Rahim (as they were running towards each other and met at the common point, so distance covered by Rahim is equal to distance pending to be covered by Ram and vice versa)
sarthak1701
Krunaal
The direct formula for this is, whenever two entities starting from opposite ends at the same time meet at a common point and the total distance they travelled is D, the ratio of their speeds \(\frac{Sa}{Sb} = \sqrt{\frac{Tb}{Ta}}\), where Tb and Ta is the time taken to reach their destination from the common point. Below is the detailed solution,

Let total distance be D, where D = d1 + d2

When Ram and Rahim meet, Ram covers d1 and Rahim covers d2

Speed of Ram = Sa; Speed of Rahim = Sb

We need to find \(\frac{Sa}{Sb}\)

When Ram and Rahim meet,

\(\frac{d1}{Sa} = \frac{d2}{Sb}\) ...............................(as time is same)

\(\frac{d1}{d2} = \frac{Sa}{Sb}\) .................................(1)

Ram takes 1 minute to cover d2, so \(Sa * 1 = d2\)

Rahim takes 4 minutes to cover d1, so \(Sb * 4 = d1\)

Subs. in (1)

\(\frac{Sb*4}{Sa*1} = \frac{Sa}{Sb}\)

\(4*Sb^2 = Sa^2\)

\(\frac{Sa}{Sb} = \frac{2}{1}\)

Answer B.
Hey could you elaborate why have you taken d2 as distance covered by ram in substitution? His distance initially assumed is d1 right?
Show more
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,586
Own Kudos:
1,079
Posts: 38,586
Kudos: 1,079
A and B are two points on a straight line. Ram runs from A to B while 10 Oct 2025, 03:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts