RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 51 of Exercise 10E

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51

A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

Let the speed of stream be x km/h

Speed of boat is 18 km/hr


Speed downstream = (18 + x)km/h


Speed upstream = (18 – x)km/h





{ using (a + b)(a – b) = a2 – b2 }


324 – x2 = 48x


x2 + 48x – 324 = 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 = 48 c = – 324


= 1. – 324 = – 324


And either of their sum or difference = b


= 48


Thus the two terms are 54 and – 6


Difference = 54 – 6 = 48


Product = 54. – 6 = – 324


x2 + 54x – 6x – 324 = 0


x(x + 54) – 6(x + 54) = 0


(x + 54)(x – 6) = 0


x = – 54 or x = 6


(but x cannot be negative)


x = 6


Hence the speed of stream is 6 km/h


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