Question : 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?
Option 1: 30
Option 2: 15
Option 3: 20
Option 4: 10
Correct Answer: 15
Solution :
Let the time required for A to complete the task alone as
B would have taken 10 hours more than A to complete the task.
Working together, A and B can complete the task in 12 hours.
The combined rate of A and B is
The combined rate of A and B is the sum of their rates.
From equation (i)
⇒
⇒
⇒
From equation (i)
So, B would take 30 hours to complete the entire task. To do 50% of the task, B would take 50% of 30 hours, which is 15 hours.
Hence, the correct answer is 15.
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