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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?

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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


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1 answers

24 vote
Answered by on | Votes 24 |

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)/(x+ 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.
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