Answer :

Let the speed of Deccan Queen be x km/h

Speed of another train = (x – 20)km/h


According to the question




taking LCM




4800 = x2 – 20x cross multiplying


x2 – 20x – 4800 = 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 = – 20 c = – 4800


= 1. – 4800 = – 4800


And either of their sum or difference = b


= – 20


Thus the two terms are – 80 and 60


Difference = – 80 + 60 = – 20


Product = – 80.60 = – 4800


x2 – 80x + 60x – 4800 = 0


x(x – 80) + 60(x – 80) = 0


(x – 80) (x + 60) = 0


x = 80 or x = – 60 (but x cannot be negative)


Hence the speed of Deccan Queen is 80 km/hr


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