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Quantitative Aptitude -Time,Speed and Distance- A train from Hwh to Puri!

train problems TSD1

PSA_LEVEL-UP_QNR41. The distance from Howrah (HWH) to Puri (PUR) along a new railway track is 600 km. Two trains A (from HWH to PUR) and B (from PUR to HWH) leave simultaneously from both these stations travelling towards the other station with constant speed. They meet each other exactly after 6 hours. As soon as they meet, the train A slows down by 10 kmph and the train B speeds up by 10 kmph. If both the trains reach their destinations at the same time, then what are the initial speeds of the trains A and B (in kmph) respectively?

(1) 50, 50
(2) 55, 45
(3) 45, 55
(4) 60, 40

Ans:

Let M be the point where trains A and B meet after 6 hrs.

Time taken to meet = Total distance/Relative Speed
=>Relative Speed = 600 km/6 hrs= 100 km/h

If speed of train A is Sa and that of train B is Sb, then
Sa+Sb=100 km/h.

|HWH|——————-|M|——————————————|PUR|
<………x……………..> <……………………..600-x…….>

Also, (600-x)= distance covered by train B (from PUR to M) in 6 hrs = Sb*6
=> x= 600-6*Sb

Now, train A moves from M to PUR station with an increased speed of (Sa-10) km/h in time= (600-x)/(Sa-10).
Similarly, train B moves from M to HWH station with a decreased speed of (Sb+10) km/h in time= (x)/(Sb+10).

According to the question,
(600-x)/(Sa-10) = (x)/(Sb+10)

=> 600Sb + 6000 -xSb -10x= xSa -10x
=> 600Sb + 6000 = x(Sa+Sb)
=>600Sb + 6000 = x(100)
=>600Sb + 6000 = (600-6Sb)(100)
=>1200Sb= 54000
=>12Sb= 540
=>Sb= 45 km/h.

Sa=55 km/h.

Option (2).

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