A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Let B take x days to complete the work
Work one by B in one day 
A will take (x – 10) days to complete the work
Work one by B in one day 
According to the question
x2 – 10x = 12 (2x – 10)
x2 – 10x = 24x – 120
x2 – 34x + 120 = 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 = – 34 c = 120
= 1.120 = 120
And either of their sum or difference = b
= – 34
Thus the two terms are – 30 and – 4
Sum = – 30 – 4 = – 34
Product = – 30. – 4 = 120
x2 – 30x – 4x + 120 = 0
x(x – 30) – 4(x – 30) = 0
(x – 30) (x – 4) = 0
x = 30 or x = 4
x = 30 (number of days to complete the work by B cannot be less than A)
B completes the work in 30 days