7 men can complete a piece of work in 6 days while 4 women can do it in 14 days. In how many days can 2 women and 2 men complete it?
12 days
Let the amount of work done by one man in one day be m and by one woman be w.
From the given, 7 men complete the work in 6 days, so the total work is:
Work = 7 × 6 × m = 42m
Similarly, 4 women complete the work in 14 days, so the total work is:
Work = 4 × 14 × w = 56w
Thus, we have the equations:
42m = 56w
m = (56 / 42) × w = 4/3 w
Now, 2 men and 2 women complete the work in d days. The total work is:
Work = 2 × m × d + 2 × w × d
Substituting m = 4/3 w, we get:
Work = 2 × (4/3)w × d + 2 × w × d = (8/3)w × d + 2w × d
Work = w × d × (8/3 + 2) = w × d × (14/3)
Equating this with the total work (42m = 56w), we have:
w × d × (14/3) = 56w
d × (14/3) = 56
d = 56 × (3 / 14) = 12 days
Thus, 2 women and 2 men can complete the work in 12 days.
Important Questions from Time and Work
Surbhi can do a piece of work in 24 days. She completed 3/8 of the work and then left it. Amit can complete the remaining work in 10 days. Working together, they will complete 125% of the same work in:
Rama and Hari can together finish a piece of work in 15 day. Rama works twice as fast as Hari, then Hari alone can finish work in :
Anil, Deepak and Dinesh together can complete a work in 35 days. Anil and Dinesh together can complete the same work in 60 days. In how many days Deepak alone can complete the same work?
Anu is four times as good as Binni in completing a task. Together they finish the same task in 7 hours. In how many hours will Anu alone complete the task?
P, Q and R can complete a work in 10 days, 20 days and 30 days, respectively, working alone. How soon can the work be completed if P is assisted by Q and R on alternate days?
