Amit can do a piece of work in 45 days, but Bharath can do the same work in 5 days less, than Amit, when working alone. Amit and Bharath both started the work together but Bharath left after some days and Amit finished the remaining work in 56 days with half of his efficiency but he did the work with Bharath with his complete efficiency. For how many days they had worked together?

     $AmitBharatNo.of Days4540Efficiency2.22Percent(=\frac{1}{45})2.5 Percent(=\frac{1}{40})$

Amit did the work in 56 days =  $56\times \frac{1}{45\times 2}=\frac{28}{45}$ 

Therefore, Rest work 17/45 was done by Amit and Bharath =  $\frac{\frac{17}{45}}{\frac{17}{360}}$ = 8 days

( since Amit and Bharath  do the work in one day =  $\frac{1}{45}+\frac{1}{40}=\frac{17}{360}$)