P is 1.5 times as efficient as Q. Q takes 5 more days than P to complete the work. It is also known that Q takes 3 days more than R to complete the work. All of them began working but P leaves the work after 2 days from the start and R leaves 3 days before completing the work. How long does it take to complete the work?
6
9
7.5
8.4
Answers
P is 1.5 times as efficient as Q. Q takes 5 more days than P to complete the work. It is also known that Q takes 3 days more than R to complete the work. All of them began working but P leaves the work after 2 days from the start and R leaves 3 days before completing the work. How long does it take to complete the work?
6
9
7.5
8.4
Step-by-step explanation:
A is 1.5 times efficient than B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?
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8 Answers

Nahas Ellathu Parambil, HVAC QC Engineer
Answered October 30, 2017
Let B take D no: of days to finish the work.
So, A takes D-8 days to finish.
Efficiency of A = 1/(D-8)
Efficiency of B = 1/D
Given that A is 1.5 times efficient than B.
ie
(1/D-8)/(1/D) = 1.5
or D = 24.
ie in one day A can finish 1/16 of work. B can finish 1/24 of work.
If A and B work on alternate days, they finish 1/16 +1/24 = 5/ 48 of the work in 2 days.
no: of days (alternate) required to finish work = 1/(5/48) = 9.6 days for each person, that is 19.2 days.
Now , we cross check the status after 19 days. A have worked for 10 days and B for 9 days.
Amount of work finished after 19 days = 10 x (1/16) + 9 x (1/24) = 1.
That means, at the end of exactly 19 days, the work would finish.
A work for 10 days and B for 9 days.
The value 19.2 we got is because of the lesser efficiency of B.