B would have taken 10 hours more than what A would have taken to complete a task if each of them worked alone. Working together they can complete the task in 12 hours. How many hours would B take to do 50% of the task?

Let say, A took x hrs to complete the task .

So, B will take (x+10) hrs to complete it .

So, According to question :

$$\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\ .$$

or, $$12\left(x+x+10\right)=x^2+10x\ .$$

or, $$x^2-14x-120\ =0\ .$$

or, $$x^2-20x+14x-120\ =0\ .$$

or, $$\left(x-20\right)\left(x+14\right)=0\ .$$

So, either $$x=20\ or\ \ x=-14\ .$$

So, x should be 20 .

So, B takes 30 hrs to complete the work .

So, B will take 15 hrs to complete the 50% of work .

B is correct choice.