Question
'A' and 'B' alone can complete a work in 9 days and 18
days, respectively. Find the time taken by them to complete the work if they work on alternate days starting with 'A'.Solution
ATQ, Let the total work be the LCM of 9 and 18, which is 18 units. Efficiency of 'A' = 18/9=2 units/day Efficiency of 'B' = 18/18=1 unit/day If the work was started by 'A', then on the first day, work completed by 'A' = 2 units On the next day, work completed by 'B' = 1 unit Therefore, in two days, the amount of work completed by 'A' and 'B' = 2 + 1 = 3 units So, in 12 days, work completed by 'A' and 'B' = 3 × 6 = 18 units Therefore, total time taken by them to complete the work = 12 days
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