A and B together can do a piece of work in 15 days; B and C together can do it in 12 days; C and A can do it in 20 days. How long will they take to finish the work, working together? Also, find the number of days taken by each to do the same work, working alone?
Answers
Answer:
all together= 10 days
A alone= 60 days
B alone = 20 days
C alone= 30 days
Step-by-step explanation:
A+B can do the work in 15 days
B+C ************************* 12 days
C+A ************************* 20 days
so LET the work be LCM of 15,12&20
i.e. work = 60
now
efficiency = w/t
hence
efficiency of
A+B = 60/15 = 4
B+C = 60/12 = 5
C+A = 60/20 = 3
NOW,
efficiency of
A+B+B+C+C+A = 4+5+3
OR
2(A+B+C) = 12
OR
A+B+C = 12/2 = 6
NOW
We have
efficiency of A+B+C = 6
&
efficiency of A+B = 4
hence
efficiency of C = 6-4 = 2
&
efficiency of B+C = 5 => B+ 2 = 5
efficiency of B = 5-2 = 3
& similarly efficiency of A = 4-3 = 1
now
A alone can do the work in
=> 60/1 = 60 days
B alone can do the work in
=> 60/3 = 20 days
C alone can do the work in
=> 60/2 = 30 days
and all A, B, C working together can complete the work in
=> 60/6 = 10 days