A is 60% more efficient than B. In how many days will A and B working together complete a piece of work which A alone takes 15 days to finish?

Given,
A is 60% more efficient of B Means,
$$\eqalign{ & {\text{A}} = {\text{B}} + 60\% \,{\text{of B}} \cr & {\text{A}} = {\text{B}} + \frac{{60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{100{\text{B}} + 60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{160{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{8{\text{B}}}}{5} \cr} $$
A can complete whole work in 15 days. So,
One day work of A = $$\frac{1}{{15}}$$
One day work of A = $$\frac{{8{\text{B}}}}{5}$$ = $$\frac{1}{{15}}$$
One day work of B = $$\frac{5}{{120}}$$ = $$\frac{1}{{24}}$$
One day work, (A + B) = $$ \frac{1}{{15}} + \frac{1}{{24}}$$
One day work, (A + B) = $$\frac{{24 + 15}}{{360}}$$   = $$\frac{{39}}{{360}}$$
So, Time taken to finish the work by A and B together = $$\frac{{360}}{{39}}$$ = $$\frac{{120}}{{13}}$$ days

Alternatively
We can solve it through percentage method
Given,
A = $$\frac{{8{\text{B}}}}{5}$$
A can complete whole work in 15 days
Work rate of A = $$\frac{{100}}{{15}}$$ = 6.66% per day
Work rate of $$\frac{{8{\text{B}}}}{5}$$ = 6.66%
Work rate of B = 4.16% per day
Work rate of (A + B) = 6.66 + 4.16 = 10.82% per day
So, A and B can complete 100% work in $$\frac{{120}}{{13}}$$ days