Akbar, benoit, and cinder take 20, 80, 160 days respectively to complete a work. if each work one day
Answers
Akbar takes 20 days
⇒ 1 day = 1/20 of the work
Benoit takes 80 days
⇒ 1 day = 1/80 of the work
Cinder takes 160 days
⇒ 1 day = 1/160 of the work
Assuming Akbar started working on day 1, Benoit on day 2 and Cinder on day 3. And the cycle repeats.
Find the work done in 1 cycle ( 3 days):
work done = 1/20 + 1/80 + 1/60 = 11/160
Find the number of cycles (3 days) needed to complete the work:
11/160 of work = 1 cycle
1/160 of the work = 1/11 cycle
160/160 of the work = 1/11 x 160 = 14 with remaining 3/80 of work not done
Therefore, there are 14 cycles (of 3 days) and still remaining 3/80 of the work
Akbar can do 1/20 of the work in a day
3/80 < 1/20 ⇒ So Akbar needs to work one more than to finish the work
Total number of days needed:
14 cycles + 1 day = 14 (3) + 1 = 43 days
Answer: It will take 43 to finish the work