Train number 21 and Train number 22 travelling at the same constant

Question

Train number  21  and Train number  22  travelling at the same constant rate towards each other along a parallel track between Station  P  and Station  Q  met at a point  M . If Train number  21  starts from Station  P  at 3:00 p.m, then at what time will it reach Station  Q  ?

(1) Train number 21 starts from Station P and takes 3 hours to reach M, while Train number 22 starts from Station Q and takes 2 hours to reach M. 
 (2) Train number 22 started from Station Q at 2:00 p.m.

stne · Answer

Let the speed of both trains be  s . Note: Both the trains are travelling at same speed.

(1) Train number 21 starts from Station P and takes 3 hours to reach M, while Train number 22 starts from Station Q and takes 2 hours to reach M.

3s+2s= 5s , Thus the total distance is  5s

Time taken by train  p = \frac{5s}{s} = 5  hrs.

Hence train  21  will reach Q by  8:00  p.m.

SUFF.

(2) Train number 22 started from Station Q at 2:00 p.m.

Lets say they took  t  hrs to meet and both have speed  s.

Then  ts + (t+1)s = d

However we cannot solve  \frac{2ts+1}{s}

INSUFF.

Ans A

Hope it helped.

shubs80 · Answer

This questions seems to be flawed , if both trains have same speed , they are bound to take equal amount of time to reach meeting point.Its not possible that train 22 just reaches in 2 hours

siddhantvarma · Answer

shubs80  You don't know how far point M is from Station P and Q. M doesn't lie midway between Station P and Q. If Station P and Station Q lie at different distances from point M, both trains will take different times to reach M even if they have the same speed. Hope that clarifies.

shubs80 · Answer

Since M is the meeting point , and speeds are same , M has to be the mid-point,try with numbers

siddhantvarma · Answer

shubs80  Did you also assume that both the trains start at the same time? Say the distance between P and Q is 30 km. Let's say both Train 21 and 22 have a speed of 10km/hour. Let's say point M is at distance x from P and y from Q. According to you, x should be equal to y. That will only happen if the time taken by both the trains is the same to cover distances x and y respectively.

Let's say Train 21 takes time  t_1  to cover distance x and Train 22 takes time  t_2  to convert distance y.

For train 21: 10 = x/ t_1 
For train 22: 10 = y/ t_2

From the above we can say x/ t_1  = y/ t_2 , but we can't say x = y unless we know  t_1  =  t_2 
In fact, Statement (1) gives you two different times, ie  t_1  =  3 and  t_2  = 2. If you plug in those values, you get x = 30 and y = 20 in our case. Clearly x is not equal to y. Hence your assumption that M has to be the mid-point of P and Q is wrong.

Vittal123 · Answer

it's possible only if train 22 started earlier. Question does not mention that they start at the same time.

Train number 21 and Train number 22 travelling at the same constant

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Train number 21 and Train number 22 travelling at the same constant

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