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# Points A, P, Q and B lie on the same line such that P, Q and B are, re

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Math Expert
Joined: 02 Sep 2009
Posts: 64249
Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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03 Apr 2020, 07:55
00:00

Difficulty:

45% (medium)

Question Stats:

76% (02:41) correct 24% (02:26) wrong based on 37 sessions

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Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A. 1 : 4
B. 2 : 9
C. 1 : 2
D. 2 : 7
E. 2 : 9

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Senior Manager
Joined: 18 Jan 2020
Posts: 342
Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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03 Apr 2020, 08:02
Speed is direct proportional to distance.
Car 3 cover 100m when Car 1 covered 200.-----(1)
Also, Car 3 covered 200m when Car 2 does 100m. ------(2)
So, the ratio will be Car1:Car2:Car3
400:100:200 (equating statements)
So the ratio of speed of Car 2 : Car 1 is 1:4
So OA is A

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Senior Manager
Joined: 14 Oct 2019
Posts: 406
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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03 Apr 2020, 13:57
Car 3 meets car 1 at Q, which is 200 km from A.

Therefore, at the time of their meeting car 1 must have travelled 200 km and car 3 must have travelled 100 km.

As the time is same, ratio of speed of car 1 to speed of car 3 = 2 : 1.

Car 3 meets car 2 at P, which is 100 km from A.

Therefore, at the time of their meeting car 2 must have travelled 100 km and car 3 must have travelled 200 km.

As the time is same, ratio of speed of car 2 to speed of car 3 = 1 : 2.

Speed of car 1 : speed of car 3 = 2 : 1

And speed of car 2 : speed of car 3 = 1 : 2

So, speed of car 1 : speed of car 2 : speed of car 3 = 4 : 1 : 2

speed of car 2 : speed of car 1 = 1 : 4

Senior Manager
Joined: 14 Oct 2019
Posts: 406
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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03 Apr 2020, 14:01
method II : let , speed of car 1,2,3 be v1,v2,v3 respectively.
from s=vt formula,
200/v1 = 100/v3 ___________ (1)
100/v2 = 200/v3 ___________(2)
from (1) and (2)
v2/v1 = 1: 4 [ANSWER A ]
GMATWhiz Representative
Joined: 07 May 2019
Posts: 709
Location: India
Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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04 Apr 2020, 00:27
Bunuel wrote:
Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A. 1 : 4
B. 2 : 9
C. 1 : 2
D. 2 : 7
E. 2 : 9

Are You Up For the Challenge: 700 Level Questions

Solution

• Let the speed of car 1, car 2 and car 3 be $$s_1, s_2$$ and $$s_3$$respectively.
• We know that $$distance = speed * time$$,
o And if time is constant, speed is directly proportional to distance.
• Now, Car 1 and Car 3 meets at Q.
o Since, both started simultaneously, time is constant.
o Thus, Ratio of speed of car 1 and car 2 = Ratio of distance travelled by car 1 and car 2,
 $$s_1 : s_3 = 200:100 = 2:1 …………Eq.(i)$$
• Also, Car 2 and Car 3 meets at P,
o Again, both started at same time, so time is constant.
o Thus, Ratio of speed of car 3 and car 2 = Ratio of distance travelled by car 3 and car 2,
 $$s_3 : s_2 = 200:100 = 2:1 …………Eq.(ii)$$
• Now, to equate the ratios, we can rewrite Eq.(i) as
o $$s_1 : s_3 = 2:1 = 4:2$$
• Now, from the above equation and eq.(ii), we get,
o $$s_1 : s_3: s_2 = 4 : 2 :1$$
 $$s_2 : s_1 = 1:4$$
Thus, the correct answer is Option A.
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Joined: 03 Jun 2019
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Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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04 Apr 2020, 08:00
Bunuel wrote:
Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A. 1 : 4
B. 2 : 9
C. 1 : 2
D. 2 : 7
E. 2 : 9

Are You Up For the Challenge: 700 Level Questions

Given: Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P.

Asked: If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A------100 km----------P---------100 km--------Q----------100 km----------B
Car1->----------------------------------------Car1+3
Car2->----------------Car2+3
-----------------------------------------------------------------------------<-Car 3

Since all cars start at the same time, once they meet their speeds are directly proportional to the distance covered.

Let the speed of car1 , car2 & car3 be v1, v2 & v3 respectively

v1/v3 = 200/100 = 2/1 = 2
v2/v3 = 100/200 = 1/2

v2/v1 = (v2/v3)/(v1/v3) = (1/2)/2 = 1/4

IMO A
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
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Joined: 30 Jun 2019
Posts: 209
Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re  [#permalink]

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04 Apr 2020, 12:29
Car1 goes 200, Car 3 goes 100
Car 3 goes 200, Car 2 goes 100

C1:C3 = 2:1
C3:C2 = 2:1

C1:C3:C2 = 2:1 2:1 = 4:2 2:1 = 4:2:1
C1:C2 = 4:1
Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re   [#permalink] 04 Apr 2020, 12:29