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

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 ]

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.

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

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

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