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Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
03 Sep 2011, 07:22

14

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

65% (04:44) correct
35% (04:19) wrong based on 114 sessions

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.

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.

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.

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]

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) _________________

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

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
03 Oct 2013, 09:40

why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet. so not necessary that anand would have travelled same distance as ram did.?

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
03 Oct 2013, 13:26

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

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
06 Oct 2013, 05:19

sunny3011 wrote:

why the distance covered is 2(90-x) ? 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(90-x)? I understand why we need the first (90-x), but why is it assumed that they meet at the same point X when they're headed back?

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
17 Oct 2013, 03:39

1

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.

why the distance covered is 2(90-x) ? 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(90-x)? I understand why we need the first (90-x), 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 1393 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.

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
17 Oct 2013, 08:00

3

This post received KUDOS

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 90-6x covered twice in 6 hours. => 12x + 18x = 2(90-6x) giving 2x (remember this is the speed of anand and not just x) = 60/7

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
17 Oct 2013, 08:56

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.

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
17 Oct 2013, 08:58

Expert's post

AccipiterQ wrote:

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.

Check solutions above. You can use only one variable to solve. _________________

Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
24 Jun 2014, 21:05

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=(90-x)/9 and s2=(90+x)/8 where s1 and s2 are the speed of Anand and Ram resp. (90-x) /9 / (90+x)/8 = 2/3 From the above equations we get s1=60/7 _________________

Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]
27 Jun 2015, 23:39

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