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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
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.