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प्रश्न
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
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उत्तर
Let the speed of the fast train be x km/hrthen
the speed of the slow train be = (x - 10)km/hr
Time taken by the fast train to cover 200km = `200/xhr`
Time taken by the slow train to cover 200km =`200/(x-10)hr`
Therefore,
`200/(x-10)-200/x=1`
`rArr(200x-200(x-10))/(x(x-10))=1`
`rArr(200x-200x+2000)/(x^2-10x)=1`
`rArr2000/(x^2-10x)=1`
⇒ 2000 = x2 - 10x
⇒ x2 - 10 - 2000 = 0
⇒ x2 - 50x + 40x - 2000 = 0
⇒ x(x - 50) + 40(x - 50) = 0
⇒ (x - 50)(x + 40) = 0
So, either
x - 50 = 0
x = 50
Or
x + 40 = 0
x = -40
But, the speed of the train can never be negative.
Thus, when x = 50 then
= x - 10
= 50 - 10
= 40
Hence, the speed of the fast train is x = 50km/hr
and the speed of the slow train is x = 40km/hr respectively.
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