Working alone, A will take 8 more hours to complete the job than that taken by both A and B working together. Similarly, if B worked alone, he will take 4 1\2 more hours to complete the job than when he works with A. How long will they take to complete the job if they work together?

Explanation:

When A and B work together, let them take ‘x’ hours to complete the task.

Working alone, let A alone take ‘a’ more hours and let B take ‘b’ more hours to complete the task.

Therefore, A will take (x + a) hours to complete the task.

And B will take (x + b) hours to complete the task.

In an hour, A will complete 1\x+a th of the task.

Similarly, in an hour B will complete 1\x+b th of the task

Hence, when they work together they will complete

= {1\x+a+1 x+b} th of the task in an hour. …(1)

But, we know that they complete the task in hours if they work together

Or, 1\xth of the work will complete in an hour. …(2)

As (1) and (2) are equal, we get 1\x=1\x+a+1\x+b

Solving the equation, we get x^2= ab or x=ab−−√ab

In this question, a = 8 hrs and b = 4 1\2 hours.

Thus, the time taken by A and B to complete the job, working together, x=√ab=√8×9\2 = 6 hours.