A and B can do a piece of work in 10 days B and C in 15 days and C and a in 20 days they all worked at first 6 days and then a loose and B and C go on together for 4 days more if 3 then lives how long will it take to complete the work
Answers
Answer:
A + B do 1/10 of work;
B+ C do 1/15,
C + A do 1/20
so 2 (A+ B + C) do 1/10 + 1/15+1/20 = 13/60 of the work.
So A + B + C do 13/120 of work in a day
. If all work for 6 days,
13*6/120 = 78/120 or 39/60 th of work will be completed,
leaving 21/60 or 7/20 of work to be completed.
B and C working together will complete 4*1/15 = 4/15 of the work leaving (7/20 - 4/15) = 5/60 = 1/12 of work yet to be completed.
A + B + C do 13/120 of work a day and A + B do 1/10 of work. So C does 13/120 - 1/10 = 1/120 of the work. So to complete 1/12 work, C will take (1/12)/(1/120) = 10 days
Answer:
Work Rate of A and B Together = 100/10 = 10% per day.
Work Rate of B and C = 100/15 = 6.66% per day.
Work Rate of A and C = 100/20 = 5% per day.
Now,
(A + B + B +C + C +A) = 10 + 6.66 + 5
2*(A + B + C) = 21.66
A + B + C = 10.83% per day.
C = 10.83 - (A +B).
Work Rate of C,
C = 0.83 per day.
Work rate of A, B and C together = 10.83% per day.
Work Completed in 6 days = 10.83 * 6 = 64.98%.
Work completed by B and C in 4 days = 6.66 * 4 = 26.64%.
Rest work = 100 - 64.98 - 26.64 = 8.38%.
Now, C will complete these work in,
= 8.38/0.83 = 10 days.