A and B can do a work in 15 days and 20 days respectively. If they work together for 4 days, then the fraction of the work that is left is:

$\frac{8}{15}$

A can do a work in 15 days and B in 20 days

They work on it together for 4 days

Total work = Number of days × 1 day's work (Efficiency)

∴ Total work = LCM (15, 20) = 60 unit

1 day's work of A = 60/15 = 4 unit

1 day's work of B = 60/20 = 3 unit

1 day's work of (A + B) together = 4 + 3 = 7 unit

Now,

They work on it together for 4 days

∴ Total work completed in 4 days = 4 × 7 = 28 unit

Work left = 60 - 28 = 32 

The fraction of work that is left = 160/300 = 8/15.