Answer :

Let the usual speed of the train be x km/h

Time taken to cover 300 km =


New speed of train = x + 5 km/h


Time taken to cover 90 km =


According to the question






750 = x2 + 5x


x2 + 5x – 750 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 5 c = – 750


= 1. – 750 = – 750


And either of their sum or difference = b


= 5


Thus the two terms are – 25 and 30


Difference = 30 – 25 = 5


Product = 30. – 25 = – 750


x2 + 30x – 25x – 750 = 0


x(x + 30) – 25(x + 30) = 0


(x + 30) (x – 25) = 0


x = – 30 or x = 25 (but x cannot be negative)


x = 25


Hence the usual speed of the train is 25 km/h


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