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Quantitative Aptitude -Time,Speed and Distance- Buses on parallel lanes!!!

PSA_LEVEL-UP_QNR47.There are two parallel lanes between bus stops A and B. One of the lanes is actually the main road and the other one, a service lane. Two long buses are plying on these two lanes. Bus M is 50 metres long and takes the service lane while Bus N is 75 metres long and is on the main road. When they are going in the same direction, the faster bus takes 60 seconds to pass the other completely. When they are going in the opposite directions they pass each other completely in 10 seconds. What is the speed of the slower bus and which bus (M or N) is the faster one?

a) 5.21 m/s; Bus N
b) 7.29 m/s; Bus M
c) 5.21 m/s; Cannot be determined.
d) 7.29 m/s; Cannot be determined.

Ans:

Whichever is the faster or slower bus, the distance to cover remains same i.e. 50+75 or 125 metres. Below diagram will give you some idea. Also this distance is same whether it is the “overtaking” scenario or simple “crossing” one. The only difference is “relative speed”.

time speed and distance buses on parallel lanes

 

Let speed of faster bus be Sf and that of the slower one, Sl.

Relative speed when faster bus overtakes the slower one:
———————————————————————————–
Time taken = Distance/Relative speed

=> 60 = 125/(Sf -Sl)
=>(Sf -Sl) = 125/60
Relative speed when both buses cross each other completely:
—————————————————————————————
Time taken = Distance/Relative speed

=> 10 = 125/(Sf + Sl)
=>(Sf +Sl) = 125/10,

From the above two equations, 2Sf = 125[1/60 + 1/10] = 125*7/60
Sf= 125*7/120 = 7.29 m/s.

Sl= 125/10 – 7.29 = 12.5 – 7.29 = 5.21 m/s.

We cannot determine which Bus (M or N) is slower as there is inadequate data in the question. Option C.

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