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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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03 Apr 2020, 07:55
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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 Are You Up For the Challenge: 700 Level Questions
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Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re
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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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Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re
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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
correct answer is A



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



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Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re
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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 QuestionsSolution • 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 \(s_1 : s_3: s_2 = 4 : 2 :1\)
Thus, the correct answer is Option A.
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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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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 QuestionsGiven: 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 A100 kmP100 kmQ100 kmB 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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Re: Points A, P, Q and B lie on the same line such that P, Q and B are, re
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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
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