Question

A, B and C can do a work in 20, 45 and 120 days
respectively. They started the work. A left 10 days
before and B left 5 days before the completion
of work. In how many days is the total work completed?​

Answer 1

Answer:

Answer is 20 days.

It is given that to complete the whole work, A alone takes 20 days, B alone takes 45 days, and C alone takes 120 days.

Let T be the total number of days required to complete the whole work when A, B & C all do together. Then according to the given data,

Fraction of the whole work done by A = (T - 10) / 20 …… (1)

Fraction of the whole work done by B = (T - 5) / 45 …… (2)

Fraction of the whole work done by C = T / 120 …… (3)

Hence summing (1), (2) & (3) we get

(T - 10) / 20 + (T - 5) / 45 + T / 120 = 1

or 18T - 180 + 8T - 40 + 3T = 360 or 29T = 580 or T = 20 days

Answer 2

Let the work be completed in N-days.

So (N-10)/20 + (N-5)/45 + N/120

So (N-10)18 + (N-5)8 + 3N = 360

29N = 580

So N = 20

Therefore the whole work was completed in 20 days.