A and B together can do a certain work in x days. Working alone, A and B can do the same work in (x + 8) and (x + 18) days, respectively. A and B together will complete $\frac{5}{6}$ of the same work in: 

10 days

A + B = x days,

A = (x + 8) days,     ..(1)

B = (x + 18) days,   ..(2)

⇒ Value of x will be under root of product of these 2 numbers = 

√(8 + 18) = √144 = 12 

⇒ x = 12.

Now putting value of x in (1) and (2),

⇒ A = (12 + 8) = 20 days

⇒ B = (12 + 18) = 30 days,

⇒ \(\frac{5}{6}\) of total work = \(\frac{5}{6}\) x 60 = 50 units.

⇒ Time taken by A + B to complete 50 units of work = \(\frac{50}{5}\) = 10 days.     ..(\(\frac{Work}{Efficiency}\) = Time)