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?
1). 30
2). 15
3). 20
4). 10
Let A would have taken x hours to complete the task,
⇒ According to given condition B would take (x + 10) hours to complete the task
⇒ Work done in one day by A and B will be 1/x and 1/(x + 10) units
Since working together they take 12 hours to complete the task,
⇒ 1/x + 1/(x + 10) = 1/12
⇒ (2x + 10)/(x2 + 10x) = 1/12
⇒ 24x + 120 = x2 + 10x
⇒ x2 - 14x - 120 = 0
⇒ (x - 20) (x + 6) = 0
⇒ x = 20, -6
∴ B will take 30 hours to complete the task and 15 hours to complete 50% task.