Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 19 of Exercise 10E
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19
Divide 27 into two parts such that the sum of their reciprocals is 3/20.
Let the two parts be x and (27 – x)
According to given condition,
On taking the LCM
On Cross multiplying
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 = – 27 c = 180
= 1. – 180 = – 180
And either of their sum or difference = b
= – 27
Thus the two terms are – 15 and – 12
Sum = – 15 – 12 = – 27
Product = – 15. – 12 = 180
x (x – 15) – 12(x – 15) = 0
(x – 15) (x – 12) = 0
(x – 15) = 0 or (x – 12) = 0
x = 15 or x = 12
Case I: when x = 12
27 – x = 27 – 12 = 15
Case II: when x = 15
27 – x = 27 – 15 = 12
Hence required numbers are 12 and 15.
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.
