A and B work together to complete the rest of a job in 7 days. However,$$\frac{{37}}{{100}}$$ of the job was already done. Also the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work ?

$$\eqalign{ & {\text{Total work}} = 100 \cr & {\text{Remaining work}} \cr & = 100 - 37 \cr & = 63 \cr & {\text{5A}} = {\text{4B}} \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{4}{5}{\text{ efficiency}} \cr & {\text{Total efficiency of A}} + {\text{B}} = 9 \cr & {\text{Work done by in 7 days}} \cr & = 9 \times 7 \cr & = 63 \cr & \therefore {\text{Time taken by B}} \cr & = \frac{{100}}{5} \cr & = 20{\text{ days}} \cr} $$