A, B and C can individually complete some work in 20, 15, and 12 days respectively. The y start the work but A, B, and C leave 2, 3, and 4 days respectively before the scheduled completion of work. Every time a worker leaves, he is replaced by someone who works till the end with half the efficiency of the leaving worker. Also, an extra worker is added after all three original workers leave and the efficiency of this worker is equal to the sum of efficiencies of A, B and C. In how many days is the work actually completed?a)daysb)daysc)daysd)daysCorrect answer is option 'C'. Can you explain this answer?

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A, B and C can individually complete some work in 20, 15, and 12 days respectively. The y start the work but A, B, and C leave 2, 3, and 4 days respectively before the scheduled completion of work. Every time a worker leaves, he is replaced by someone who works till the end with half the efficiency of the leaving worker. Also, an extra worker is added after all three original workers leave and the efficiency of this worker is equal to the sum of efficiencies of A, B and C. In how many days is the work actually completed?

a)
days
b)
days
c)
days
d)
days

Correct answer is option 'C'. Can you explain this answer?

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A, B and C can individually complete some work in 20, 15, and 12 days ...

If the total work to be done is 120 units, A, B and C respectively do 6, 8 and 10 units of work per day i.e. they together do 24 units of work per day.
Hence, scheduled time for completion of work = 120/24 = 5 days Now, they start together and A, B and C leave 2, 3 and 4 days before the scheduled completion of work.
Hence, A, B and C work for 3, 2 and 1 day(s) respectively.
Since all the options show the actual time between 4 days and 5 days, first find the work done in 4 days.
Day 1: A + B + C = 24 units

Day 2: A + B + C’s replacement = 6 + 8 + (10/2) = 19 units

Day 3: A + B’s replacement + C’s replacement = 6 + (8/2) + (10/2) = 15 units Day 4: A’s replacement + B’s replacement + C’s replacement + Extra worker = (6/2) + (8/2) + (10/2)+ (6 + 8 + 10) = 36 units.
Total work done in 4 days = 24 + 19 + 15 + 36 = 94 units The remaining 26 units of work have to be done by the three replacement workers and the extra worker, who can together do 36 units of work per day (as seen from day 4).
Time taken to complete 26 units = 26/36 = 13/18 days.

Hence, option 3.

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