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.

bumpbot · Answer

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

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