A and B can complete a work in 10 and 100 days respectively each. How long will it take to finish the work when they work on alternate days starting with B?
Explanation:
Let the total work to be done = LCM(10, 100) = 100 units.
Efficiency of A = 100/10 = 10 units/day
Efficiency of B = 100/100 = 1 unit/day.
Since they work on alternate days, they would work in cycles of 2 days.
Work done by (A + B) in 1 cycle of two days = 10 + 1 = 11 units/cycle.
Hence, they take 100/11 =9(1/11) cycles to complete the work.
Since, the no. of cycles is a fraction, we will have to analyze the last incomplete cycle.
Work done in 9 complete cycles = 9 × 11 = 99.
Time that has passed till 9 cycles = 9 × 2 = 18 days.
Hence, work left for the 10th incomplete cycle = 100 – 99 = 1.
Since B starts the work, he would work on 19th day and would complete 1 unit of the work. Hence the work gets completed at the end of 19th day.
The work gets completed in 19 days.
Hence, 19.
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