Time, Speed & Distance
Aptitude

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Q.

Two stations $A$ and $B$ are 110 km apart on a straight line. One train starts from $A$ at 7 am and travel towards $B$ at 20 km/hr speed. Another train starts from $B$ at 8 am and travel towards $A$ at 25 km/hr speed. At what time will they meet?

 A.

9 am

 B.

10 am

 C.

11 am

 D.

None of these

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Solution:
Option(B) is correct

In 1 hour (7 am to 8 am) tarin from station A travels 20 km distance and reaches to $C$, (say).

$A$ ----------------- $C$ ---------------$B$
7 am --------------------------------- 8 am

$AC$ = 20 km, $CB$ = 90 km

Distance travelled in 1 hour = 20 km

Remaining distance =$110−20$ = 90 km

\(\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}\)

\(\dfrac{90}{20+25}=2\) hours

So, time = 8 am + 2 am = 10 am


(7) Comment(s)


Imran
 ()

Why do we add $2$ hours with that of second train's starting time?

Are we not supposed to add with the firsts'?


Shireen
 ()

Hey Imran, time is added AFTER $A$ has traveled for 1 hour (i.e. time is 8 AM now). Now it takes two more hours after 8 AM when both $A$ and $B$ travel at the speed of 20 km/hr and 25 km/hr respectively.

That is why 2 hours time is added after 8 AM and not 7 AM, it has nothing to do with the first or second train's time.

Hope that helps :)

Imran
 ()

thanks shireen..i got it..


Madhu
 ()

Thank you, Aman, now I got it


Aman
 ()

Pleasure is all mine, Madhu :)


Madhu
 ()

how do we get AC =20


Aman
 ()

Train from station $B$ starts AFTER 1 hour (at 8 am). So in that time, train from station $A$ travels till point $C$ for 1 hour, with the speed of 20 km/hr. Which makes distance $AC=20$ km.

Hope this helps.