Question
Two workers, 'X' and 'Y', can
complete a task on their own in 18 days and 30 days, respectively. If they work on alternate days, beginning with 'X', how many days will it take to finish the work?Solution
Let the total work be the LCM of [18, 30] = 90 units. So, the efficiency of 'X' = (90/18) = 5 units/day. Efficiency of 'Y' = (90/30) = 3 units/day. Work done on the first day by 'X' = 5 units. Work done on the second day by 'Y' = 3 units. So, the work done in two days = 5 + 3 = 8 units. Amount of work done in 22 days = 8 × 11 = 88 units. The remaining 2 units will be completed by 'X' on the 23rd day.
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