A and B can do a job in 12 days. After 2 days they are assisted by C who works at the same rates as A. The work takes 25/4 days more to finish. In how many days will B alone do the work ?
Answers
A+B 's job in one day= 1/12
similarly, A+B+C's job in one day=4/25
so C's job in one day alone= (4/25)-(1/12)=(48-25)/300= 13/300
as C's job per day is equivalent to A's,
B's alone job= (1/12)-(13/300)=(25-13)/300=12/300=1/25
so B can alone complete the job in 25 days.
Answer: 30 days
Step-by-step explanation:
Work done by (A + B) in one day = 1/12 of the whole. ….(1)
Work done by (A+B) in 2 days = 2 × 1/12 = 1/6 of the whole.
Work remaining to be done after (A+B) have worked on it for 2 days = 1 - 1/6 = 5/6.
Now A, and B are joined by C, (who is as as efficient as A i.e C =A).
A +B +C finish the remaining 5/6 of the whole work in another 25/4 days
Work done by A +B + C in one day = (5/6) ÷ (25/4) = 2/15 of the whole. Now as C= A,
Work done by 2A + B in one day = 2/15 ……(2)
Subtracting (1) from (2), we would get the work done by A alone in 1 day.
Work done by A working alone in 1 day =(2/15) -(1/12) = (8–5)/60 = 3/60 = 1/20 of the whole……..(3)
So A working alone could finish the work in 20 days.
Subtracting (3) from (1) we can get work done by B working alone in 1 day
Work done by B in one day = (1/12) -(1/20) = (5–3)/60 = 2/60 = 1/30 of the whole ——-(4).
So working alone B could finish the work in 30 days.