Three
small
pumps and a large pump are filling a tank. Each of the three small pump works
at 2/3 the rate of the large pump. If all four pumps work at the same time,
they should fill the tank in what fraction of the time that would have taken
the large pump alone?

a) 4/7

b)
1/3

c)
2/3

d)
3/4

Let
the work done by the big pump in one hour be 3 units.
Therefore, work done by each of the small pumps in one hour = 2 units. Let the
total work to be done in filling the tank be 9 units.
Therefore, time taken by the big pump if it operates alone = 9/3 = 3
hours.
If all the pumps operate together, the work done in one hour = 3 + 2*3 = 9
units.
Together, all of them can fill the tank in 1 hour.
Required ratio = 1/3