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Q : The speeds of 3 Cars A, B and C were compared. Car A and B were observed for identical durations, while Car C was observed for 2 seconds longer. During its period of observation, Car B traveled three times the distance Car A traveled, and therefore Car B was found to be faster than Car A by 2000 kilometers per second. Car C had an identical speed as that of Car A , but because Car C was observed for a longer period, it traveled five times the distance Car A traveled during Car A's inspection.
Car A traveled how many kilometers during its observation?

A: 1000 B: 2500 C: 500 D: 1500 E: 1600/3

[spoiler]MY ANS IS A BUT OA. IS A (500)[/spoiler]

[cans]

A,B for x sec and C for x+2 sec
distance by A=y
B=3y
thus 3y/x - y/x = 2000 -> y/x=1000
C's speed = y/x = 5y/(x+2)
x=1/2. thus y = 500
IMO C

[navami]

Speed of A = A
Speed of B = B
Let assume time observed = t

Speed of C = C

C is observed for t+2 secs.

B = 3A ---(1)

B - A = 2000. ---(2)

From equation (1) and (2) 2A = 2000
A = 1000 KM/sec


C = =A <-- As per the question
C has travelled 5 times the distance of A
C*(t+2 ) = 5 *A*t
and C = A so we can write
A ( t+2) = 5* A * t
or (t+2) = 5t
t = 1/2 sec

so A travells t * A
= 1/2 * 1000
500 KM

ANS