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?

Explanation:-

Given,
A is 60% more efficient of B Means,
A = B + 60% of B.
A = $$\frac{{8{\text{B}}}}{5}$$
A can complete whole work in 15 days. So,
One day work of A = $$\frac{1}{{15}}$$
One day work of $$\frac{{8{\text{B}}}}{5}$$ = $$\frac{1}{{15}}$$
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 = $$\frac{{360}}{{39}}$$ = $$\frac{{120}}{{13}}$$

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