Question

A contractor has two teams of workers: team a and team

b. team a can complete a job in 12 days and team b can do the same job in 36 days. team a starts working on the job and team b joins team a after four days. the team a withdraws after two more days. for how many more days should team b work to complete the job?

Answer 1

Rate of team a = 1/12


Rate of team b = 1/36

Combined rate = 1/12 + 1/36 = 1/9

Fraction done in 4 days = 4x1/12 = 1/3


Remaining fraction =  1-1/3 = 2/3

Two days working together
Fraction done = 2x1/9 = 2/9


Remaining fraction = 2/3 – 2/9 = 4/9


Number of days it will take team b to complete the job = (4/9)/(1/36)
                                                                                       = 16 days

Answer 2

Ans. 16

Solution(*STEP BY STEP):

Let total worker in team A be x

Let total worker in team B be y

Given 12 x = 36 y

x = 3y

Per worker work done per day be W.

total work 36 × W × y

36Wy = 6 × Wx + MWy

M = 2 + Number of more days.

36 y = 18 y + My

M = 18y + My

M = 18

Hence 16 more days ( as M was 2 + number of more days)