hemant_rajput wrote:Q17 . A tank in X apartment is full of water is fitted with pumps of equal capacity. Besides it is also fitted with a certain no. of inlet pipes which are always kept open. When tank is full, 10 pumps of equal capacity empty the tank in 12 hrs. , while 15 pumps of the same capacity empty the tank in 6 hrs. In how much time would 25 pump of the same capacity empty the tank, if the tank is initially full?(All the pipes pouring water into the tank are always open)
a. 3
b. 2.5
c. 4
d. 3.5
e. 5.5
[spoiler]oa:d[/spoiler]
Every hour:
The pumps pump units OUT of the tank.
The inlet pushes units INTO the tank.
When the pumps and the inlet work simultaneously for a certain amount of time, the ENTIRE VOLUME OF THE TANK is removed.
Thus:
Tank volume = total amount PUMPED OUT - total amount PUSHED IN.
Let x = the amount PUSHED IN by the inlet each hour.
Case 1: 10 pumps empty the tank in 12 hrs
In 12 hours:
The amount PUMPED OUT by 10 pumps = r*t = 10*12 = 120.
The amount PUSHED IN by the inlet = 12x.
Thus:
Tank volume = total pumped out - total pushed in = 120 - 12x.
Case 2: 15 pumps empty the tank in 6 hrs
In 6 hours:
The amount PUMPED OUT by 15 pumps = r*t = 15*6 = 90.
The amount PUSHED IN by the inlet = 6x.
Thus:
Tank volume = total pumped out - total pumped in = 90 - 6x.
Since the volume is the same in each case, we get:
120 - 12x = 90 - 6x
30 = 6x
x = 5.
Thus:
Each hour, the amount PUSHED IN by the inlet = 5 units.
Tank volume = 90 - 6x = 90 - 6*5 = 60 units.
When 25 pumps work:
Amount PUMPED OUT by 25 pumps each hour = 25 units.
Amount PUSHED IN by the inlet each hour = 5 units.
Thus:
Net amount removed each hour = 25-5 = 20 units per hour.
Time to empty the tank = w/r = 60/20 = 3 hours.
The correct answer is
A.
Same answer as Tommy's.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
