Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 19 Oct 2010
Posts: 222
Location: India
GPA: 3

Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
Updated on: 13 Jul 2013, 07:19
2
This post received KUDOS
18
This post was BOOKMARKED
Question Stats:
68% (03:59) correct 32% (03:57) wrong based on 174 sessions
HideShow timer Statistics
Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed. (A) (45/7) kmph (B) (60/7) kmph (C) (40/7) kmph (D) (30/7) kmph (E) (65/7) kmph
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
petrifiedbutstanding
Originally posted by petrifiedbutstanding on 03 Sep 2011, 08:22.
Last edited by Bunuel on 13 Jul 2013, 07:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1903

Re: Anand's speed.. [#permalink]
Show Tags
03 Sep 2011, 08:58
11
This post received KUDOS
3
This post was BOOKMARKED
petrifiedbutstanding wrote: Found this exercise in a random book.
Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
(A). (45/7) kmph (B). (60/7) kmph (C). (40/7) kmph (D). (30/7) kmph (E). (65/7) kmph
Can someone help with this, please? Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (90x) km Anand traveled this x kms in 3 hours, making his speed x/3 kmph Ram traveled the same x kms in 2 hours, making his speed x/2 kmph So, in 6 hours: Anand will cover=6x/3=2x km Ram will cover=6x/2=3x km And between their first meeting point and second, they both together covered a distance of 2(90x) km. 2x+3x=2(90x) 5x=1802x 7x=180 x=180/7 km Anand's speed=x/3=180/(3*7)=60/7 kmph Ans: "B"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 08 Nov 2010
Posts: 358
WE 1: Business Development

Re: Anand's speed.. [#permalink]
Show Tags
04 Sep 2011, 10:00
fluke wrote: petrifiedbutstanding wrote: Found this exercise in a random book.
Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
(A). (45/7) kmph (B). (60/7) kmph (C). (40/7) kmph (D). (30/7) kmph (E). (65/7) kmph
Can someone help with this, please? Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (90x) km Anand traveled this x kms in 3 hours, making his speed x/3 kmph Ram traveled the same x kms in 2 hours, making his speed x/2 kmph So, in 6 hours: Anand will cover=6x/3=2x km Ram will cover=6x/2=3x km And between their first meeting point and second, they both together covered a distance of 2(90x) km. 2x+3x=2(90x) 5x=1802x 7x=180 x=180/7 km Anand's speed=x/3=180/(3*7)=60/7 kmph Ans: "B" Nice solution. I made it much more complicated... I used  3A=2R 8R=90+x 9A=90x solving giving the same result  but i guess it took me longer than to you and increased my chances to make mistakes...
_________________
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 04 Jun 2011
Posts: 174

Re: Anand's speed.. [#permalink]
Show Tags
04 Sep 2011, 10:08
yup nice and easy one fluke!! kudos for the wonderfully solving the problem in 3 steps



Manager
Status: Dreaming High
Joined: 24 Apr 2011
Posts: 52
Location: India
Concentration: Operations, Strategy
GPA: 3.28
WE: Project Management (Manufacturing)

Re: Anand's speed.. [#permalink]
Show Tags
04 Sep 2011, 10:30
1
This post received KUDOS
Speed of Anand =a '" Ram=r Till Anand and Ram meets, Anand travels for 3 hrs, and Ram trvels for 2 HRs When Two people meet, the distance travelled by them is equal=>> 3a = 2r which gives r = 3a/2(i) Now for next 6 hrs, Anand travels 6a Kms and Ram trvls 6r Kms. Refer the pic: ....(3a).................(6a)................................. P________________________________________Q ....(2r)....................................(6r).................... The (6r) covers the distance from ( to Q)plus( Q to  ) PQ = 90 2PQ = 180 3a + 6a + 6r + 2r = 180 9a + 8r = 180 9a + 8*3a/2 = 180 using (i) 9a + 12a = 180 a = 180/21 = 60/7 From this
_________________
[caption=]Remember: Anything that can go wrong, will go wrong.[/caption]



VP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1354
GRE 1: 1540 Q800 V740

Re: Anand's speed.. [#permalink]
Show Tags
04 Sep 2011, 11:41
3
This post received KUDOS
Let a be Anand's speed and r be Ram's speed.When Ram and Anand meet for the first time, distance travelled by them is the same => a(3) = r(2) When Ram and Anand meet for the second time, they have travelled twice the distance PQ, or 180 km, together => a(9) + r(8) = 180 Solving these equations for a, we get a = 180/21 = 60/7 km/hr =>Option (B)
_________________
GyanOne  Top MBA Rankings and MBA Admissions Blog
Top MBA Admissions Consulting  Top MiM Admissions Consulting
Premium MBA Essay ReviewBest MBA Interview PreparationExclusive GMAT coaching
Get a FREE Detailed MBA Profile Evaluation  Call us now +91 98998 31738



Manager
Joined: 19 Oct 2010
Posts: 222
Location: India
GPA: 3

Re: Anand's speed.. [#permalink]
Show Tags
07 Sep 2011, 03:01
Thank you, fluke and GynaOne. Really simple solutions!
_________________
petrifiedbutstanding



Intern
Joined: 20 Jul 2011
Posts: 8
Location: India
GPA: 3.12
WE: Information Technology (Consulting)

Re: Anand's speed.. [#permalink]
Show Tags
07 Sep 2011, 07:23
Couldn get it the first time Took more than 5 min to solve. After looking at the solution it looked easy but I was stumped Have a small doubt.. On GMAT wats the probability of facing these kind of questions ?? And at what level?? Please clarify cheers
_________________
Maverick%^%^



Intern
Joined: 06 Dec 2012
Posts: 25
Concentration: Finance, International Business
GPA: 3.5

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
03 Oct 2013, 10:40
why the distance covered is 2(90x) ? ram meets anand after 6hrs on first meet. so not necessary that anand would have travelled same distance as ram did.?
bunuel help ?



Current Student
Joined: 17 Sep 2013
Posts: 24
Location: United States
Concentration: Economics, Statistics
GPA: 3.36
WE: Analyst (Health Care)

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
03 Oct 2013, 14:26
1
This post received KUDOS
I solved it like this:
Let R = Ram's speed A = Anand's speed
Since it took Ram 2 hours to cover the same distance as Anand did in 3 hours we know
2R = 3A R = (3/2)A
We know they don't meet again for another 6 hours, at which point Anand will have been traveling for 9 hours to a distance I'll call "D". Ram will have been traveling for only 8 hours when he reaches D and the total distance he will have traveled is 90 + (90  D) = 180  D
So:
9A = D 8R = 180  D or 180  8R = D
180  8R = 9A
Substitute for R
180  8(3/2)A = 9A 180  12A = 9A 180 = 21A 60/7 = A



Current Student
Joined: 15 Sep 2013
Posts: 11

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
06 Oct 2013, 06:19
sunny3011 wrote: why the distance covered is 2(90x) ? ram meets anand after 6hrs on first meet. so not necessary that anand would have travelled same distance as ram did.?
bunuel help ? Same question: Why is it 2(90x)? I understand why we need the first (90x), but why is it assumed that they meet at the same point X when they're headed back?



Math Expert
Joined: 02 Sep 2009
Posts: 45251

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
17 Oct 2013, 04:39
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
pauc wrote: sunny3011 wrote: Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
(A) (45/7) kmph (B) (60/7) kmph (C) (40/7) kmph (D) (30/7) kmph (E) (65/7) kmph
why the distance covered is 2(90x) ? ram meets anand after 6hrs on first meet. so not necessary that anand would have travelled same distance as ram did.?
bunuel help ? Same question: Why is it 2(90x)? I understand why we need the first (90x), but why is it assumed that they meet at the same point X when they're headed back? Look at the diagram below: Attachment:
Untitled4.png [ 2.58 KiB  Viewed 2761 times ]
Blue dot is the second meeting point. In blue is the distance covered by Anand after the first meeting. In green is the distance covered by Ram after the first meeting. Their sum is twice 90x. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 15 Aug 2013
Posts: 58

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
17 Oct 2013, 09:00
6
This post received KUDOS
1
This post was BOOKMARKED
Here is a quick approach since we know the time taken by anand : time taken by ram (same distance when they meet after 3 hrs) = 3 : 2. therefore, ratio of their speed= 2 : 3. Let speed be 2x, 3x. Now in three hours distance covered = 6x. remaining 906x covered twice in 6 hours. => 12x + 18x = 2(906x) giving 2x (remember this is the speed of anand and not just x) = 60/7



Manager
Joined: 26 Sep 2013
Posts: 204
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
17 Oct 2013, 09:56
I don't get this problem at all; you don't know how long it takes Ram to reach the end point and then turn back, so you can't calculate anything for certain...there's too many variables here.



Math Expert
Joined: 02 Sep 2009
Posts: 45251

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
17 Oct 2013, 09:58



Director
Joined: 17 Dec 2012
Posts: 635
Location: India

Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
24 Jun 2014, 22:05
Since Anand takes 3 hrs to travel the distance that Ram travels in 2 hrs their speed is in the ratio 2:3. We also know s1=(90x)/9 and s2=(90+x)/8 where s1 and s2 are the speed of Anand and Ram resp. (90x) /9 / (90+x)/8 = 2/3 From the above equations we get s1=60/7
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com/bestonlinegrepreparation.php
Improve Intuition and Your Score Systematic Approaches



NonHuman User
Joined: 09 Sep 2013
Posts: 6812

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
Show Tags
31 Jan 2018, 17:00
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Anand starts from a point P towards point Q, where PQ = 90
[#permalink]
31 Jan 2018, 17:00






