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
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Correct Answer: 15
Solution :
Let the time required for A to complete the task alone as $x$ hours and for B as $y$ hours.
B would have taken 10 hours more than A to complete the task.
$y = x + 10$ ..................(i)
Working together, A and B can complete the task in 12 hours.
The combined rate of A and B is $\frac{1}{12}$ tasks per hour.
The combined rate of A and B is the sum of their rates.
$\frac{1}{x} + \frac{1}{y} = \frac{1}{12}$
From equation (i)
$\frac{1}{x} + \frac{1}{x + 10} = \frac{1}{12}$
⇒ $x^2-14x-120=0$
⇒ $(x+6)(x-20)=0$
⇒ $x=20$ [since $x$ can't be negative]
From equation (i)
$y = x+ 10 = 30$
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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