# A train covers a

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

Time taken to cover 90 km = New speed of train = x + 15 km/h

Time taken to cover 90 km = According to the question    2700 = x2 + 15x

x2 + 15x – 2700 = 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 = 15 c = – 2700

= 1. – 2700 = – 2700

And either of their sum or difference = b

= 15

Thus the two terms are – 45 and 60

Difference = 60 – 45 = 15

Product = 60. – 45 = – 2700

x2 + 60x – 45x – 2700 = 0

x(x + 60) – 45(x + 60) = 0

(x + 60) (x – 45) = 0

x = – 60 or x = 45 (but x cannot be negative)

x = 45

Hence the original speed of the train is 45 km/h

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 