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# Problems on Trains Questions

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An express A starts at 2:30 pm from Karnal station and travel towards Sirsa station at a speed of 80 km per hour. Another express B starts at 4:30 pm from Karnal to Sirsa at the speed of 100 km per hour. How far away from station Karnal will the two trains meet?

A400 km

B500 km.

C800 km

D600 km.

Explanation:

Train A starts at 2:30 pm from KARNAL to SIRSA.
Train B starts at 4:30 pm from KARNAL to SIRSA.
Lets assume they meet x hours after 2:30 pm.
So, distance traveled by A in x hours or by B in (x-2) hours.
Given, speed of A = 80 km/hr
Distance traveled by A in x hours at 80km/hr ------------ (1)
and Speed of B = 100 km/hr.
Distance traveled by B in (x-2) hours at 100km/hr = 100(x-2) km ------ (2)
As, trains meet after x hours and i.e distance covered by train A in x hours equals distance covered by train B in (x-2) hours.
From eq. (1) and (2)
80x = (x-2)100
=> 20x = 200
x = 10 hours.
So, hey meet after 10 hours from 2:30 pm.
Hence, required distance = 80x = 80 * 10 = 800 km.

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Chennai express starts at 8 am from A towards B and Mumbai express starts at 8 am from B towards A. After their meet, Chennai express takes 18 hours to reach B and Mumbai express takes 8 hours to reach A. Then which of the following is their speed's ratio?

A1:02

B2:03

C1:03

DNone of these

Explanation:

Let's name both trains as A and B. Then,
Formula Used: âˆš(A's speed) : âˆš(B's speed) = âˆšb : âˆša
âˆš(A's speed) : âˆš(B's speed) = âˆš8 : âˆš18 => 2âˆš2 : 3âˆš2 => 2 : 3.

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A train P starts from Delhi at 8 pm, reaches its destination UP at 1:00 am. Another train Q starts from UP at 8:00 pm and reaches Delhi at 2:00 am. The two trains P and Q will cross each other at :

A10:45 AM

B10:45 PM

C12.45 pm

D12.45 am

Explanation:

Lets assume distance between UP and Delhi = X km.
So, Time taken by P to reach UP = 8 pm to 1 am = 5 hours.
=> Speed of P = X/5 km/hr.
Time taken by Q to reach Delhi = 8 pm to 2 am = 6 hours.
=> Speed of Q = X/6 km/hr.
Lets assume them meet Y hours after 8 pm.
Distance covered by P at Y hours at X/5 km/hr speed = Y * X/5 km
Distance covered by Q at Y hours at X/6 km/hr = Y * X/6 km.
As given train are running in opposit direction so
=> XY/5 + XY/6 = X
XY (1/5 + 1/6 ) = X
Y (1/5 + 1/6 ) = 1
Y (11/30) = 1
11*Y = 30.
Y = 30/11 = 2.72 hours
Therefore, they meet after 2.72 hours from 8 pm.
That is, 8 pm + 2 hours + 45 minutes (nearly).
Hence, the answer is 10.45 pm.

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A train started from station 'A' and proceeded towards station 'B' at a speed of 48 Km/hr. Forty-five minutes later another train started from station 'B' and proceeded towards station 'A' at 50 Km/hr. If the distance between the two stations is 232 Km, at what distance from station 'A' will the trains meet?

A160KM

B108KM

C132KM

D144KM

Explanation:

Given, Distance between A and B = 232 KM
Speed of A = 48 km/hr. and Speed of B = 50 Km/hr.
Distance covered by A and B = (48*x)+(50*(x-(45/60)))=232
Therefore, x=11/4
So,distance covered by A = 48*x=48*(11/4)=132 Km

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A train travels at an average of 50 miles per hour for 2x1/2 hours and then travels at a speed of 70 miles per hour for 1x1/2 hours. How far did the train travels in the entire 4 hours?

A120 miles

B150 miles

C200 miles

D230 miles

Explanation:

Total distance=50*5/2+70*3/2= 230miles

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At 10:00 am 2 trains started travelling towards each other from station 287 miles apart they passed each other at 1:30 pm the same dayy .if average speed of the faster train exceeded by 6 miles /hr what is speed of faster train in miles/hr:

A34 miles/hrs.

B38 miles/hrs.

C44 miles/hrs.

D40 miles/hrs.

Explanation:

Lets assume the speed of slower train = x miles/hrs.
So, speed of faster train is = (x+6) miles/hrs.
Given, passed each other at 1:30 PM i.e after 3 1/2 hrs.
Both train travelling towards each other so total relative speed = x+(x+6) = (2x+6)
So, 287/(2x+6) = 7/2 => 574 = 14x + 42
=> 14x = 542 => x = ~38

So spee of faster train = (x+6) miles/hrs. = 44 miles/hrs.

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The time a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?

A3:1

B1:3

C1:2

D2:1

Explanation:

Lets assume speed of freight train = X Km/hr
speed of passenger train = Y Km/hr.
and sum of their length = D Km.
When trains are running in same direction:
so Time = D/(X-Y) ---------- (1)
When trains are running in opposite direction:
So, Time = D/(X+Y) --------- (2)
By eq. (1) & (2)
[D/(X-Y)] = 2 * [D/(X+Y)]
=> 2X-2Y = X+Y
=> X = 3Y
=> X:Y = 3:1

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A train runs first half of the distance at 40 km/hr and the remaining half at 60 km/hr. What is the average speed for the entire journey?

A28 Km/hr.

B52 Km/hr.

C48 Km/hr.

DNone of these

Explanation:

Avg speed=2xy/(x+y)
=2*40*60/100 = 48 Km/hr.

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Two trains A and B start simultaneously from stations X and Y towards each other respectively. After meeting at a point between X and Y,train A reaches station Y in 9 hours and train B reaches station X in 4 hours from the time they have met each other. If the speed of trainA is 36 km/hr, what is the speed of train B?

A24 km/hr

B54 km/hr

C81 km/hr

D16 km/hr

Explanation:

Naming the trains as A and B. Then,
(A's speed) : (B's speed) = (b : a)^.5
where b and a is the time taken by trains B and A, to reach their destination after they meet.
hence,
36/B's speed = (4: 9)^.5
=> B's speed = 54km/hr

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A train overtakes 2 persons walking at 3 km/hr and 5 km/hr respectively in the same direction and completely passes them in 8 seconds and 10 seconds respectively. Find the speed of the train.

A12 Km/hr

B13 Km/hr

C23Km/hr

D21 Km/hr

Explanation:

Lets assume train speed = x km/hr.
Relative speed respect to 1 person and train= (x-3)
Relative speed respect to 2 person and train= (x-5)
Dist. = speed * time
8(x-3)= 10(x-5)
=> x=13Km/hr

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