Mugdha and Mayuri, working together, can complete a job in 18 days. However, Mayuri
works alone and leaves after completing two-fifths of the job and then Mugdha takes over and completes the remaining work by herself. As a result, the duo could complete the job in 39 days. How many days would Mugdha alone have taken to do the job if Mayuri worked faster than Mugdha?

Let, Mugdha complete the whole work in $$x$$ days and Mayuri complete the whole work in $$y$$ days
Given, they can complete a job in 18 days working together i.e
= $$\frac{1}{x} + \frac{1}{y} = 18$$ .........(1)
And also given that mayuri completes $$\frac{2}{5}$$th of the work while $$\frac{3}{5}$$th will be completed by mugdha
so, $$\frac{2}{5}y + \frac{3}{5}x = 39$$.........(2)
After solving equations (1) and (2) we get,