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?
Answer & explanation
Correct answer: option 2
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