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?

Solution (By Examveda Team)

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

⇒ A + B complete the work in 12 hours
$$\eqalign{ & \therefore \frac{{x\left( {10 + x} \right)}}{{10 + x + x}} = 12 \cr & 10x + {x^2} = 120 + 24x \cr & {x^2} - 14x - 120 = 0 \cr} $$
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