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A bus covers a distance of 180 km at a certain speed. By, increasing the speed by 30 kmph, the bus can reach it's destination an hour before. The original speed of the bus is -

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Question

A bus covers a distance of 180 km at a certain speed. By, increasing the speed by 30 kmph, the bus can reach it's destination an hour before. The original speed of the bus is

Options

  • 60 kmph

  • 150 kmph

  • 30 kmph

  • None of these

MCQ

Solution

60 kmph

Explanation:

Method-1: Let speed of the bus be x kmph, then `180/x - 180/(x + 30)` = 1

On solving we get, `x^2 + 30x - 5400` = 0

`x^2 + 90x - 60x - 5400` = 0

`x(x + 90) - 60(x + 90)` = 0

Hence `x` = 60 or – 90, 

so `x` = 60 kmph

Method-2: Consider your options, which would take much less time.

Checking option (1) If speed of the bus = 60 kmph. original time = 180/60 = 3 hrs, new speed = 60 + 30 = 90 kmph and new time = 180/90 = 2 hrs, which Is 1 hour less. hence 1 is the correct option.

Checking option 2 if s = 150kmph. then original time = 180/ 150 = 6/5 hours = 1 hr 12minutes

New speed = 150 + 30 = 180 kmph and new time = 180/180 = 1 hour. By increasing the speed by 30 kmph the bus is taking 12 minutes less while in the question it is given 1 hour less. hence option 2 is wrong. Similarly, options 3 and 4 are also wrong.

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Time, Speed and Distance (Entrance Exam)
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