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

x^{2} – 10x = 12 (2x – 10)

x^{2} – 10x = 24x – 120

x^{2} – 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

x^{2} – 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

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