Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 51 of Exercise 10E
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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
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
