Train A takes 45 minutes more than train B to travel a distance of 450 km. Due to engine trouble speed of train B falls by a quarter, so it takes 30 minutes more than Train A to complete the same journey. What is the speed of Train A (in km/hr)?
A) 90 B) 120 C) 100 D) 110
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Answer:
it's answer is c 100 km per hour
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Required speed of train A is 100 km / hr.
Step-by-step explanation:
Let the time taken to complete the whole journey by train B be a hours.
So, time taken by train A to be complete the journey should be [ a + ( 45 x 1 / 60 ) ] hours i.e. ( a + 3 / 4 ) hours.
Thus,
= > Speed of train A = ( Distance / time )
= > Speed of train A = 450 / ( a + 3 / 4 ) km / hr
According to the question :
Due to engine trouble speed of train B falls by a quarter, so it takes 30
minutes more than train A to complete the same journey.
Thus,
= > Speed of train B due to trouble = 450 / a km / hr - 1 / 4 of 450 / a km / hr
= > Speed of train B due to trouble = ( 450 / a - 1 / 4 of 450 / a ) km / hr
= > Speed of train B due to trouble = 675 / 2a km / hr ... ( 1 )
Given, due to trouble in engine, now,
= > Time taken by train B = time taken by train A + 30 minutes
= > Time taken by train B due to trouble = a + 3 / 4 + ( 30 x 1 / 60 ) hr
= > Time taken by train B due to trouble = a + 3 / 4 + 1 / 2 hr
= > Time taken by train B due to trouble = ( a + 5 / 4 ) hr
From this, speed of train B after trouble = 450 / ( a + 5 / 4 ) ....( 2 )
Comparing ( 1 ) & ( 2 ) :
= > 675 / 2a = 450 / ( a + 5 / 4 )
= > 675 / 2a = ( 450 x 4 ) / ( 4a + 5 )
= > 675( 4a + 5 ) = 450 x 4 x 2a
= > 2700a + 3375 = 3600a
= > 3375 = 900a
= > 15 / 4 = a
Hence the speed of train A is 450 / ( 15 / 4 + 3 / 4 ) km / hr = 450 / ( 18 / 4 ) km / hr = 100 km / hr.
Hence the required speed of train A is 100 km / hr.
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