A and B can complete a task in 30 days when working together. After A and B have been working together
for 11 days, B is called away and A himself completes the task in the next 28 days. Had A been working alone,
the number of days taken by him to complete the task would have been:
A. 44 4/9
B. 44
C. 343 4/9
D. 45
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(A+B)*30=total work(Tw)
(A+B)*11=11days work (11Dw)
Tw-11Dw=remaining work
(A+B)30-(A+B)11=(A+B)*19
Given A complete (A+B)19 work in 28 days
A*28=(A+B)*19
28A=19B+19A
9A=19B
B=9/19A
From above Tw =(A+B)*30
=(A+9/19A)*30
=28/19A*30
=840/19 A
We know Tw=efficiency *day
A=efficiency of A
Day = 840/19=44 and 4/19
A and B can complete a task in 30 days when working together. So they perform 1/30 of the work in 1 day. After performing for 11 days, the amount of work already done becomes 11×1/30=11/30. Hence the amount of work left be 1-11/30=19/30.
Now, A completes the left work in 28 days. This gives,
19(X)/30 = 28
=> X = 28×30/19
=> X = 840/19
=> X = 44 and 4/19.
Or, its nearest equivalent answer provided,
44 4/9.
A and B can complete the work in 30 days. So,
Work Rate of A and B together = 100/30 = 3.33% per day.
In 11 days, they have completed = 3.33 * 11= 36.63% of the work.
Rest Work = 100 - 36.63 = 63.37%.
63.37% work has been completed by A in 28 days. Thus,
Work rate of A = 63.37/28 = 2.26% per day.
Now, A alone can the entire work in = 100/2.26 = 44 . 24 days = 44 (4/9) days (Approx.)