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?

Answer: Option B

Let A completes the work in $$x$$ hours
∴ B completes the work in $$x$$ + 10 hours

⇒ A + B complete the work in 12 hours
$$\begin{array}{rl}& \therefore \frac{x\left(10+x\right)}{10+x+x}=12\\ & 10x+x^2=120+24x\\ & x^2-14x-120=0\end{array}$$
On solving, $$x$$ = 20 hours
∴ B will complete whole work in 20 + 10 = 30 hours
Hence, 50% of work will be completed in 15 hours