321 Views

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


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

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.

Know More About

Related Questions

Amity Online MBA
Apply
Apply for an Online MBA from Amity Online.
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books