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प्रश्न
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
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उत्तर
Let the original speed of train be x km/hr. Then,
Increased speed of the train = (x + 15)km/hr
Time taken by the train under usual speed to cover 90 km = `90/x`hr
Time taken by the train under increased speed to cover 90 km = `90/(x+15)`hr
Therefore,
`90/x-90/(x+15)=30/60`
`(90(x+15)-90x)/(x(x+15))=1/2`
`(90x+1350-90x)/(x^2+15x)=1/2`
`1350/(x^2+15x)=1/2`
1350(2) = x2 + 15x
2700 = x2 + 15x
x2 + 15x - 2700 = 0
x2 - 45x + 60x - 2700 = 0
x(x - 45) + 60(x - 45) = 0
(x - 45)(x + 60) = 0
So, either
x - 45 = 0
x = 45
Or
x + 60 = 0
x = -60
But, the speed of the train can never be negative.
Hence, the original speed of train is x = 45 km/hr
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