Discussion

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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