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Problem on Trains

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Question
SSCCGLENQA12043289
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A man travels 450 km to his home partly by train and partly by car. He takes 8 hours 40 minutes if he travels 240 km by train and rest by car. He takes 20 minutes more if he travels 180 km by train and the rest by car. The speed of the car in km/hr is

  • 45

  • 50

  • 60

  • 48

Solution

A.

45

Let the speed of train be x kmph.
Speed of car  = y kmph.
Case I, 
               Time space equals space Distance over Speed
rightwards double arrow space space space 240 over straight x space plus space 210 over straight y space equals space 8 40 over 60 space equals space 8 2 over 3 rightwards double arrow space space 240 over straight x plus 210 over straight y space equals space 26 over 3 space space space space space... left parenthesis straight i right parenthesis     
Case II,
      180 over straight x space plus space 270 over straight y space equals space 9 space space space space space space... left parenthesis ii right parenthesis
Multiply equation (i) by 3 - Multiply equation (ii) by 4,
     rightwards double arrow space space space 720 over straight x space plus space 630 over straight y space minus space 720 over straight x space minus space 1080 over straight y rightwards double arrow space space space fraction numerator negative 450 over denominator straight y end fraction space equals space minus 10 rightwards double arrow space space space straight y space equals space 45 space kmph.

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Question
SSCCGLENQA12043290
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A train 'B' speeding with 100 kmph crosses another train C, running in the same direction, in 2 minutes. If the length of the train B and C be 150 metre and 250 metre respectively, what is the speed of the train C (in kmph)?

  • 75

  • 88

  • 95

  • 110

Solution

B.

88

Let the speed of train C be x kmph.
∴  Relative speed of B = (100 - x) kmph.
Relative space Time space equals space fraction numerator Length space of space both space trains over denominator Relative space Speed end fraction
rightwards double arrow space space 2 over 60 space equals space fraction numerator open parentheses begin display style fraction numerator 150 plus 250 over denominator 1000 end fraction end style close parentheses over denominator 100 minus straight x end fraction rightwards double arrow space space 1 over 30 space equals space fraction numerator 2 over denominator 5 left parenthesis 100 minus straight x right parenthesis end fraction rightwards double arrow space space space 1 over 6 space equals space fraction numerator 2 over denominator left parenthesis 100 minus straight x right parenthesis end fraction rightwards double arrow space space 100 minus straight x space equals space 12 rightwards double arrow space space straight x space equals space 100 minus space 12 space equals space 88 space kmph.

Question
SSCCGLENQA12042984
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A train covers a distance between A and station B in 45 minutes, If the speed of the train is reduced by 5 km per hr, then the same distance is covered in 48 minutes. The distance between stations A and B is

  • 60 km

  • 64 km

  • 80 km

  • 55 km

Solution

A.

60 km

Let the distance between stations be x km.
∴  Speed of train = fraction numerator straight x over denominator begin display style 45 over 60 end style end fraction space equals space fraction numerator 4 straight x over denominator 3 end fraction space kmph
Now, speed is reduced by 5 km/hr, 
therefore space space space space fraction numerator straight x over denominator begin display style fraction numerator 4 straight x over denominator 3 end fraction end style minus 5 end fraction space equals space space 48 over 60 rightwards double arrow space space space fraction numerator 3 straight x over denominator 4 straight x minus 15 end fraction space equals space 4 over 5 rightwards double arrow space space space 16 straight x space minus space 60 space equals space 15 straight x rightwards double arrow space space space straight x space equals space 60 space km

Question
SSCCGLENQA12043090
Wired Faculty App

A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120 m behind in 18 seconds. The speed of the second train is

  • 26 km/hr

  • 35 km/hr

  • 36 km/hr

  • 63 km/hr

Solution

C.

36 km/hr

Relative distance = 120 m
Relative Time (t) = 18 seconds
Relative speed = open parentheses 120 over 18 cross times 18 over 5 close parentheses equals space space 24 space km divided by hr
∴   Speed of second train = 60 - 24 = 36 km/hr

Question
SSCCGLENQA12042060
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A train with a uniform speed crosses a pole in 2 seconds and a bridge of length 250m in 7 seconds. The length of the train isstraight x over 2 straight m

  • 150 m

  • 120 m

  • 100 m

  • 80 m

Solution

C.

100 m

Let the length of the train  be x metre, then
Speed of a train = straight x over 2 straight m ...(i)
When it crosses a bridge, then
Speed of a train = fraction numerator straight x plus 250 over denominator 7 end fraction  ...(ii)
According to the question,
rightwards double arrow space space space straight x over 2 space equals space fraction numerator straight x plus 250 over denominator 7 end fraction rightwards double arrow space space space 7 straight x space equals space 2 straight x space plus space 500 rightwards double arrow space space 5 straight x space equals space 500 rightwards double arrow space space straight x space space equals space 100 space metre

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