A is more efficient than B and they together can complete a work in 24 days. Had A done 50% of the work and then B, the remaining work, then the work would have been done in 50 days. B alone will complete 40% of the same work in:

Let A alone take x days

And B alone take y days

$$\frac{x}{2}+\frac{y}{2}$$= 50

x + y = 100

x = 100 - y

So $$\frac{1}{100-y}+\frac{1}{y}=\frac{1}{24}$$

24y + $$24\left(100-y\right)$$ = $$y\left(100-y\right)$$

24y + 2400 -24y = 100y - $$y^2$$

$$y^2-100y+2400=0$$

y = 40 OR 60

Since A is more efficient , B takes 60 days A takes 40 days

So 40% of the work will take B = $$\frac{40}{100}\times\ 60=24\ days$$ 

Hence, Option B is correct.