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02 Sep 2022, 00:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:02) correct
28%
(01:07)
wrong
based on 149
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Water is pumped into the completely empty tank at a constant rate through an inlet pipe. At the same time, there is a leak at the bottom of the tank which leaks water at a constant rate. How long it will take the tank get filled completely?
(1) Total capacity of water the tank can hold is 120 gallons.
(2) Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank, and also the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank.
(1) Total capacity of water the tank can hold is 120 gallons.
(2) Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank, and also the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank.
02 Sep 2022, 01:02
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To find out the time taken to get filled completely, we need to know the net rate at which the tank gets filled (i.e. the rate at which the inlet fills the tank - the rate at which the lean drains the tank)
Statement 1
(1) Total capacity of water the tank can hold is 120 gallons.
We do not have any information on the rate at which the inlet pipe and the leak works. Hence we can eliminate this option.
Eliminate A and D.
Statement 2
(2) Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank, and also the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank.
We are given the rate , so lets see how can we use this option to our advantage.
Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank - So in one hour the inlet pipe can fill \(\frac{1}{10}\) th of the tank (provided there is no leak)
the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank - So in one hour the leak can drain \(\frac{1}{15}\)th of the tank (provided there is no water pumped into the tank).
Now if both are at play, in hour (\(\frac{1}{10} - \frac{1}{15}\)) of the tank gets full
\(\frac{3-2}{30}\) = \(\frac{1}{30}\) of the tank gets filled each hour.
So for the complete tank to get filled completely it will take 30 hours.
This information is sufficient.
Option B
Statement 1
(1) Total capacity of water the tank can hold is 120 gallons.
We do not have any information on the rate at which the inlet pipe and the leak works. Hence we can eliminate this option.
Eliminate A and D.
Statement 2
(2) Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank, and also the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank.
We are given the rate , so lets see how can we use this option to our advantage.
Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank - So in one hour the inlet pipe can fill \(\frac{1}{10}\) th of the tank (provided there is no leak)
the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank - So in one hour the leak can drain \(\frac{1}{15}\)th of the tank (provided there is no water pumped into the tank).
Now if both are at play, in hour (\(\frac{1}{10} - \frac{1}{15}\)) of the tank gets full
\(\frac{3-2}{30}\) = \(\frac{1}{30}\) of the tank gets filled each hour.
So for the complete tank to get filled completely it will take 30 hours.
This information is sufficient.
Option B
02 Sep 2022, 23:15
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carcass
Given information: Water fills an empty tank at a constant rate through an inlet pipe and drains (again at a constant rate) through a leak at the bottom of the tank
To determine: How long will it take to fill the tank considering inlet as well the leak causing the outlet
In order the determine the time, we need to have some information about the respective constant rates at which the tank is being filled and the one at which the leak is draining the tank
(1) Total capacity of water the tank can hold is 120 gallons.
No information is provided about any of the rates and thus just having the total capacity will not help us determine the time to fill the tank
NOT SUFFICIENT
(2) Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank, and also the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank.
Inlet pipe without leak fills the tank in 10 hours => Rate of inlet = \(\frac{1}{10}\)
Leak without inlet drains the tank in 15 hours => Rate of outlet = \(\frac{1}{15}\)
So, combined rate if both are happening at the same time (inlet as well as leak) = \(\frac{1}{10} - \frac{1}{15} = \frac{1}{30}\)
Thus, it takes 30 hours for the tank to completely fill if inlet and leak are happening at the same time
SUFFICIENT
Answer - B
