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
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
