A train P leaves Bareilly at 5 am and reaches Dehradun at 9 am. Another train Q leaves Dehradun at 7

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21 Jul 2016 Time and Distance

A train P leaves Bareilly at 5 am and reaches Dehradun at 9 am. Another train Q leaves Dehradun at 7 am and reaches Bareilly at 10.30 am. At what time do the two trains cross one another.

OPtion

1) 8.26 am
2) 7.10 am
3) 8 am
4) 8.10 am
5) 7.36 am
6) 8.40 am
7) 7.56 am
8) 7.30 am
9) 8.56 am
10)None of these

Solution

Let the distance between Bareilly and Dehradun be x km and let the train meet y hours after 7 am
Clearly, P covers x km in 4 hours and Q covers x km in 7/2 hrs
Speed of P = x/4 kmph and Speed of Q = 2x/7 kmph
Distance covered by P in (y+2) hrs + Distance covered by Q in y hrs = x
x(y+2) / 4 + 2xy/7 = x
y+2 / 4 + 2y/7 = 1
y = 14/15 hrs = 14/15 * 60 min = 56 min
So the train meet at 7.56 am
Option 7)

Correct Option: 7 Best Solution (18)

sanjeet kumar   8 years AGO

Let distance be x.
Speed of train P = x/4
Speed of train Q = 2x/7.
Train meet after t hours.
According to question
xt/4 + 2x(t-2)/7 = x
So, x = 176 min.
Hence the train will meet at 7:56

Like? Yes (5) | No (1)  

Vipul kumar   8 years AGO

Let total distance be S
since both the train are started at the interval of 2 hours and first train take 4 hours to travel whole distance so when second train starts first train already travel half of the total distance so
now both tarin starts simultaneously and when they meet the distance travel by them will be S/2

S1 +S2 =S 2
(st/240 ) +(st/210) = s/2
(t/240 ) + ( t/210 = 1/2
(t/8) + (t/7) = 15
15(t/56) = 15
t=56mins after the first train starts from the middle of journey (7)
therefore the meet at 7:56 am

Like? Yes (1) | No   

Prateek khanna   8 years AGO

Time taken by P=4h. Time taken by Q=3.5h. Take product of time taken by both as a distance=14 km P covers half distance in 2 hrs,now rest will covered by both time taken by them=7/7.5=56 min so they will cross each other at 7:56 am.

Like? Yes (2) | No (1)  

Akshat Mokashi   8 years AGO

Let distance between Barielly and dehradun be y km.
Avg speed of train leaving barielly = y/4 km/hr
Avg speed of train leaving dehradun = 2y/7 km/hr converted in fraction

suppose they meet x hrs after 5 am
then xy/4 + 2y(x-2)/7=y
on solving x=44/15
ie 2 hrs 56 min
so two trains will cross each other at 7:56 am

Like? Yes (1) | No   

Siva   8 years AGO

Let the total distance be S,
Speed of P is S/4, Speed of Q is 2S/7.
The meeting point happens in second half distance of P towards Dehradun.
So the time at which the two trains meet is
t=[(S/2)÷(S/4 +2S/7)]
From calculation we obtain
t=56 min, this56min is from7am. So the two trains meet at the time 7:56am.

Like? Yes (1) | No   

ANUJ KUMAR   8 years AGO

let dist be D
we can find speed of each train in terms of D by using times given.
using relative speed of the two train, time at which they meet can be found.

Like? Yes (1) | No   

Razen Yadav   8 years AGO

let the distance between bareily and dehradun is 'x'
for train P time=x/s1=4hr ----(1)
for train Q time=x/s2=3.5hr -----(2)
taking reciprocal and add these two eq
(s1+s2)/x=15/28 ------------(3)


we know that the relative distance will be half..===x/2
then time=relative distance+relative speed
time=(x/2)/(s1+s2)
from eq 3
time=14/15 hrs
==(14/15)*60 min
==56 min
so after 7am both trains will meet after 56 min.. 7:56 am

Like? Yes (1) | No   

madanpal vishwakarma    8 years AGO

let assume the distance between two cities is 100 km

so speed of the train staring from P is =100/4 km/h

speed of the train starting from Q =100/(7/2) km /h

So Train at Q starting at 7 am so the distance covered up to 7am is 25*2 = 50km

So the remaining distance between two train at 7am is 50 km

Now the time taken by two train is same to cross each other where t is the time

(25)(t)+(200/7)(t) =50 km

so t= 0.9333333 hour =56 minume
so time to cross each other is 7 am + 56 minute = 7.56 Am

Like? Yes (2) | No (1)  

Jagdeep   8 years AGO

P covers x km in 4 hours and Q covers x km in 7/2 hours.
Speed of P= x/4 kmph and of Q=2x/7 kmph.

Distance covered by P in M+2 hours (assume at M they will meet) + Distance covered by Q in M hours = x

therefore, x/4(M+2)+2x/7(M)=x
M=14/15 hours= 56 minutes. i.e 7:56 am

Like? Yes (1) | No   

Testing Account   8 years AGO

take lcm of time and subtract distance travelled in two hr and remaining distance divide by total speed

Like? Yes | No   

Jayanth.V   8 years AGO

3 hours from 5:00am train P covers 3/4 of the distance.Train Q covers 1/4th of distance in 52mins 30sec. so 7:56am(approx)

Like? Yes | No   

Sneha C V   8 years AGO

Using logical reasoning, we know that train Q is 7.5mins faster than train P. To balance out the difference, train Q meets train P just a little before 8am.

Like? Yes | No   

DEVANSH SUBNANI   8 years AGO

Let distance between Bareilly and Dehradun is d Km
Let Bareilli be X
Let Dehradun be Y

Let first train be A
Let second train be B

Then,speed of A is (d/4)Km/hr and that of B be (2d/7)Km/hr

X______________Y(XY=d)

Relative speed=(d/4)+(2d/7)=(15d/28)Km/hr
Now distance between these trains at 7am=d-d/2=d/2
Hence,time=(d/2)/(15d/28)=(14/15)*60=56
Hence both trains cross each other at 7:56am
Hence,option(7) is the answer.

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raman gupta   8 years AGO

if i let distance between B and D is d.
after 7am distance b/w trains P and Q will d/2.hence they will meet after 56 mints.
means 7:56 A.M.

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MOHAMMAD ANSAB   8 years AGO

When at time is 7:00
P has reaached half way to the destination but Q hasnt started yet.
Now considering at time 8:00
P has reached 3/4 of the distance that is 1/4 near to the destination.
Now Q has moved a distance of 1/3.5 that is 0.28 times the total distance.
so before 8:00 they meet and it will be at 7:56

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KUMAR HARSH   8 years AGO

let distance be x
speed of P=x/4 & Q=x/(3+1/2)=2x/7
let train meet y hour after 7am
x/4(y+2)+2x/7(y)=x
by solvthis we get 56 min
so 7h+56min=7.56

Like? Yes | No   

Suman   8 years AGO

Time taken by train P and Q are 4 and 3.5 hrs respectivly.
Now,lcm of 4 and 3.5 is 14.
Take 14km( jz assumption) as distance betwn behrali and deharadun.
Wkt both train travel same distance ie 14 km.
Now,speed of train P =14/4=3.5kmph(distance / time taken)
Lly,speed of train Q=14/3.5=4kmph.
train P leaves at 5am at 3.5kmph.At 7am it ll be half way(7 km) and train Q ll leave dehradun.
Usinh commom sense,v ll cum to knw dat ans is betwn 7.30 and 8 am but close to 8 am.So, nly option is 7.56 am

Like? Yes | No (1)  

Mukund Manohar   8 years AGO

Train P takes 4 hrs and Train Q takes 7/2 hrs to travel the same distance
Since speed is inversely proportional to time,we have,
Speed of P : Speed of Q = 3.5 : 4 = 35 : 40 = 7:8
Let the speed of trains P and Q be 7k and 8k respectively
Since,P travels 4 hrs,distance between Bareilly and Dehradun = 4*7k = 28k
P starts at 5am and completes its journey in 4 hrs
=>P(travelling with speed 7k) completes distance 14k in first 2 hrs
Then,both trains are moving and we take relative speed as 7k + 8k = 15k
Time taken to travel remaining distance 14k by both trains together = 2 * (7k/15k) = 14/15 hrs = 56 minutes
The two trains cross one another at 56 minutes after 7am,i.e. at 7:56 am

Like? Yes | No (2)