A can complete a work in 9 days and B in 12 days. If they work together on it for 5 days, then the fraction of the work left is:

A’s work rate: A can complete the work in 9 days.

B’s work rate: B can complete the work in 12 days.

Time worked together: 5 days.

Work rate of A = $$\frac{1}{\text{Number of days A takes to complete the work}}$$​​

Work rate of B =$$\frac{1}{\text{Number of days B takes to complete the work}}$$​​

Total work done by A and B in 't' days = $$\left( \text{A's work rate} + \text{B's work rate} \right) \times t$$ 

A's work rate = $$\frac{1}{9}$$ ,  B's work rate = $$\frac{1}{12}$$ 

Work done in 5 days by A and B together, 

= $$5 \times \left( \frac{ 1}{9} + \frac{1}{12} \right) = 5 \times \left( \frac{7}{36}\right) = \frac{35}{36}$$ 

Now, work left = $$1 - \frac{35}{36} = \frac{1}{36}$$ 

Therefore, work left after 5 days of A + B work = $$\frac{1}{36}$$ 

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