Time and Work

[Mayur45]

Q. Two men together can complete a piece of work in 27 days. If one of them finishes the work by himself
in 72 days more than the other one, in how much time does the faster one complete it?

A)36 days B)48 days C)64 days D)72 days
Ans:- A)36 days.
How, can anyone explains pls

[Baltuilhe]

Solution:
[tex]\dfrac{1}{x}+\dfrac{1}{x+72}=\dfrac{1}{27}[/tex]

[tex]\dfrac{x+72+x}{x(x+72)}=\dfrac{1}{27}[/tex]

[tex]x^2+72x=27(2x+72)[/tex]

[tex]x^2+72x=54x+1\,944[/tex]

[tex]x^2+18x-1944=0[/tex]

[tex]x=-54\text{ or }x=36[/tex]