A can finish a piece of work in a certain number of days. B takes 45% more number of days to finish the same work alone. They worked together for 58 days and then the remaining work was done by B alone in 29 days. In how many days could A have completed the work, had he worked alone?

118

Let number of days taken by A to complete the work = 100 days

Number of days taken by B to complete the work = 100 × \(\frac{145}{100}\) = 145 days 

ratio of         A    :    B 

Time           100  :   145 

                   20   :   29

Efficiency     29    :   20    ( time and efficiency are inverse to each other )

Let efficiency of A = 29 unit/day

Let efficiency of B = 20 unit/day

Total work = Efficiency  ×  Number of days 

Work done by A and B in 58 days = ( 29 + 20 ) × 58 = 2842 unit

Remaining work which is done by B in 29 days = 29 × 20 = 580 unit 

Total work = 2842 + 580 = 3422 unit 

Time taken by A to complete the whole work = \(\frac{3422}{29}\)  =  118 days