If two bodies start from opposite direction

Question

If two bodies start to move towards each other from opposite points P and Q, they meet at 0.6D from P. Find the point of their 4th meeting.

A) 0.2D
B) 0.4D
C) 0.6D
D) 0.8D
E) 0.3D

chiron27 · Answer

Let's say the bodies starting from P and Q are A and B respectively.

When the first meet, they cover a total distance of D (0.6D by A and 0.4D by B)

For every subsequent meet, both of them will cover 2D distance combined.
(If you already know the explaination of 2D, you can skip this part)
After the first meet, A is at 0.6D mark and so is B.
A will now cover 0.4D to reach B and B will cover 0.6D to reach A -> This means they have covered D distance for now when they will start moving in opposite directions.
Both of them will now start from the ends (P and Q), so whenever they will meet, they will cover another D distance combined.
Hence, a total of 2D distance for every subsequent meet

So, total distance covered for the meets

1st -> D
2nd -> D + 2D = 3D
3rd -> 3D + 2D = 5D
4th -> 5D + 2D = 7D

A covered 0.6D distance for a total of D distance, so will cover 4.2D for 7D distance.
Since the total distance is D, A will have covered 4 complete rounds and would be at a distance of 0.2D from P.

Hope this helps.

DiveshR · Answer

Here's one way to go about it:

First, list out all the points for A:  0.6 , 0.8 (0.4 to reach point Q and then 0.2 back),  0.2 , 0.4,  1 , 0.4,  0.2 ;
Next, list out all the points for B:  0.6 , 0.2,  0.2  (0.2 to reach point P and then 0.2 back), 0.6,  1 , 0.6,  0.2 ;

Therefore, the 4th time they meet is at 0.2D.

PawanGMAT25 · Answer

How did you arrive at the conclusion that after 1st meet, they both reach at opposite ends at the same time. Have you considered speed same for both the bodies.

Raome · Answer

KarishmaB 
Can you post an answer for this?

Krunaal · Answer

Distance from P

P---0.2---0.4---0.6---0.8---Q

Distance from Q

P---0.8---0.6---0.4---0.2---Q

When P is at 0.6, Q is at 0.4 => they meet  1st time

P---0.2---0.4--- 0.6 ---0.8---Q
P---0.8---0.6--- 0.4 ---0.2---Q

When P travels more 0.6 and comes at 0.8 (0.6 to Q = 0.4 and + 0.2), Q is at 0.8

P---0.2---0.4---0.6--- 0.8 ---Q
P--- 0.8 ---0.6---0.4---0.2---Q

When P travels more 0.6 from 0.8 and comes at 0.2, Q will travel 0.4 from its 0.8 and come back at 0.8 (0.8 to P = 0.2 and + 0.2) => they meet the  2nd time

P--- 0.2 ---0.4---0.6---0.8---Q
P--- 0.8 ---0.6---0.4---0.2---Q

Now there is a  symmetry  in this,  every odd time they will meet at 0.6 from P , and  every even time they will meet at 0.2 from P

Since 4th time is an even time, they will meet at 0.2 from P i.e.  0.2D

Answer A.

KarishmaB · Answer

If this question is a sub-part of a set, the data of the set needs to be given along with it. Otherwise, it makes no sense. Assuming A and B are moving around a circle and start from diametrically opposite points P and Q and circumference is 2D and that options give distance from P. If their first meeting while moving toward each other is at a distance of 0.6D from P, it means A covered 0.6D and B covered 0.4D. So ratio of their speeds is 3:2. So every time A covers 3/5th of the circle i.e. 1.2D and B covers 2/5th of the circle i.e. 0.8D. Their fourth meeting takes place when A has covered 3.6D distance from the present point i.e. 1 full circle of 2D (and it comes back to 0.6D from P) and another 1.2D which means it reaches 0.2D ahead of P. Answer (A) Check here: https://youtu.be/Jz-mSB1xNFY

Rohit_842 · Answer

Hi ma'am, saw your video on circular distance problems, and even though I know now that A and B will meet at 5 points (3+2) in the circle, how do I know where are these points. Also if you could please help me understand that can we convert a problem which says line PQ with distance D and A and B on opposite ends and similar data into a problem which says circle with P, Q on opposite ends and circumference 2D and similar data??

If two bodies start from opposite direction

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If two bodies start from opposite direction

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards