A, B and C together can complete a work in 15 days and A alone can complete a work in 45 days and C alone

A, B and C together can complete a work in 15 days and A alone can complete a work in 45 days and C alone can complete a work in 36 days. If B and C started the work together and B increases its efficiency by 100% and C decreases its efficiency by 40%, then find the time taken by B and C together to complete the work.

a)            20 days

b)            15 days

c)            24 days

d)            18 days

e)            None of these

Sol:

1/A + 1/B + 1/C = 1/15

1/45 + 1/B + 1/36 = 1/15

1/B + (4 + 5)/180 = 1/15

1/B + 1/20 = 1/15

1/B = 1/15 – 1/20 = (4 – 3)/60 = 1/60

Required time taken = 1/(60/2) + 1/(36*5/2) =

1/30 + 1/(36 + 24) = 1/30 + 1/60 = (2 + 1)/60 =

3/60 = 1/20 = 20 days