Question

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?

Answer 1

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