Question : A and B complete a work in 24 and 30 days, respectively, working 10 hours per day. The work is to be done in two shifts. The morning shift is for 6 hours and the evening shift is for 4 hours. On the first day, A works in the morning and B works in the evening, and they interchange their shifts every day. On which day did the work get completed?
Option 1: 21st day
Option 2: 24th day
Option 3: 30th day
Option 4: 27th day
Correct Answer: 27th day
Solution :
Given:
A can complete the whole work in 24 days.
B can complete the whole work in 30 days.
Now,
Total work = LCM of 24 and 30 = 120
Efficiency of A = $\frac{120}{24}$ = 5
Efficiency of B = $\frac{120}{30}$ = 4
Since Work done by A and B in 10 hours of one day is 5 and 4 respectively.
Work done by A and B in two days = 5 + 4 = 9 days
A and B repeat the same process on all 26 days
Work completed by A and B in 26 days = 9 × 13 =117
Remaining work = 120 – 117 = 3
Efficiency of A and B in 2 days = 5 + 4 = 9
so,
3 part work will be completed in = $\frac{2}{3}$ days
The total time taken to complete the work = $26\tfrac{2}{3}$ days
So, the total work is completed on the 27th day.
Hence, the correct answer is the 27th day.
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