Two trains traveling at same speed take 10 seconds and 15 seconds resp

Question

Two trains traveling at the same speed take 10 seconds and 15 seconds respectively to cross a telegraph post. Find the time taken by the trains to cross each other if traveling in opposite directions.

1. 6 sec
2. 12 sec 
3. 12.5 sec
4. 25 sec
5. Cannot be determined

Vinit800HBS · Answer

Algebraic approach:

Let the speed be ‘x m/s’

Distance covered by first train is 10x.
Distance covered by second train is 15x.

When travelling in opposite direction, the relative speed would be ‘2x m/s’

So, total time required to cross each other is (15x + 10x)/2x = 12.5seconds

Logical approach:

Both the trains have same speeds. So in opposite direction, relative speed will become “double”. So, time required would be “half” for the same distance. Total time as of now is 10+15 seconds.
So, it will take 12.5 seconds

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HouseStark · Answer

both the trains are moving at the same speed to cross a telegraph post= V

length of 1st train=V*10
length of 2nd train=V*15

Now both trains are moving in the opposite direction, using relative motion the first train can move at 2V speed

the total distance the 1st train has to cover is the length of both trains = 10V+15V

2V=\frac{10V+15V}{t}

2V=\frac{25V}{t}

t=12.5 sec

Answer C

napolean92728 · Answer

cfc198  CAT questions have only 4 options pls remove the 5th option in this question and keep the official 4 options.

skpaul775 · Answer

let,
Speed of both trains be 'X'.

Trains are moving in opposite direction, Relative speed = 2X
now,  Total time(T) = Total Distance covered(D)/ Relative speed(Vr)
 
T = (10X+15X)/2X = 25/2
 T = 12.5 sec.

AdarshSambare · Answer

Time Speed and distance (TSD) is tricky topic as any type of situation can be made and solution get tricky, but if your concepts are clear then no need to worry. only solution solve as many types of question you can possible:

Let the trains’ speed be x m/s.
Distance covered by first train = 10x.
Distance covered by second train = 15x.

When they travel in opposite directions, relative speed = x + x = 2x.
Time to cross = (10x + 15x) / (2x) = 25x / 2x = 12.5 seconds.

Logical view: with equal speeds, relative speed doubles, so crossing time is half the time it would take if they were moving same direction; total distance 10 + 15 = 25 (in units of x), half of 25 is 12.5.
Option : 3/C

Two trains traveling at same speed take 10 seconds and 15 seconds resp

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