if 20 percent of certain quantity of work is done by A and remaining 80 percent of work by B the work will be completed on 20 days .if 80 percent of work done by B and remaining 20 percent by A the work will be completed in 30 days.if A and B work together how many days are required to complete the work
Answers
Step-by-step explanation:
If 20% os certain quantity of work is done by A the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work, if A and B work together?
A. 11 1/9
B. 10 1/9
C. 12
D. 15
The OA is A.
Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
Say A does the complete work in a days, thus A takes a/5 days to complete 20% of the work and would take 4a/5 days to complete 80% of the work.
Similarly, say B does the complete work in b days, thus B takes b/5 days to complete 20% of the work and would take 4b/5 days to complete 80% of the work.
Condition 1: 20% of a certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days.
=> a/5 + 4b/5 = 20
a + 4b = 100 ---(1)
Condition 2: 20% of a certain quantity of work is done by B and the rest 80% by A, the work is completed in 30 days.
=> 4a/5 + b/5 = 30
4a + b = 150 ---(2)
Solving (1) and (2), we get a = 100/3 days and b = 50/3 days
A's one-day work = 3/100 and B's one-day work = 3/50
Thus, A and B's one-day work (combined) = 3/100 + 3/50 = 9/100
Thus, A and B together complete (9/100)th part of the work in one day, thus they would take 100/9 = 11 1/9 days to complete the work.
The correct answer: A
Hope this helps!
-Jay