A can do a work in 10 days and B can do the same work in 15 days. If they work on it together for 4 days, then the fraction of the work that is left is:

Let's assume the total work is 30 units.

A can do a work in 10 days.

efficiency of A = $$\frac{30}{10}$$ = 3 units/day

B can do the same work in 15 days.

efficiency of B = $$\frac{30}{15}$$ = 2 units/day
If they work on it together for 4 days.

work done by both of them in 4 days = $$\left(3+2\right)\times\ 4$$

= $$5\times\ 4$$

= 20

Fraction of the work done in 4 days = $$\frac{20}{30}$$

= $$\frac{2}{3}$$

Fraction of the work that is left = $$1-\frac{2}{3}$$

= $$\frac{3-2}{3}$$

= $$\frac{1}{3}$$