Question
Worker A can build a wall alone in 30 days. When A and B
work together, they can complete the wall in 16 days. If B starts building the wall alone and works for 20 days before leaving, how many additional days will A need to finish the remaining work alone?Solution
Let the total work to be done to build the wall = L.C.M of 30 and 16 = 240 units
Then, efficiency of ‘A’ = 240 ÷ 30 = 8 units/day
Combined efficiency of ‘A’ and ‘B’ = 240 ÷ 16 = 15 units/day
So, efficiency of ‘B’ = 15 – 8 = 7 units/day
Work done by ‘B’ in 20 days = 7 × 20 = 140 units
Remaining work = 240 – 140 = 100 units
Time taken by ‘A’ to complete the remaining work = 100 ÷ 8 = 12.5 days
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