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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 27th days.
Given that
A and B complete a work in 24 and 30 days, respectively,
Working hours per day = 10
The morning shift = 6 hours
The evening shift = 4 hours
Total work = LCM (24, 30) = 120
The efficiency of A = 120/24 = 5
The efficiency of B = 120/30 = 4
On the first day, A works in the morning and B works in the evening,
They interchange their shifts every day
In 2 days, work is done by A and B = 5 + 4 = 9
In 26 days, work is done by A and B = 9 × 13 = 117
The remaining work = 120 - 117 = 3
As we know,
A and B complete 9 works in 2 days
So, A and B complete the remaining work 3 in = 2/3 days
Hence, the total work is completed in = 26(2/3) days i.e. 27th days