Time taken to empty the cistern

[gmattesttaker2]

Hello,

Can you please assist with this? This is from Veritas practice test:

There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?


OA: 4 hours


I tried to solve as follows:


For inlet A, rate is 1/3
For inlet B, rate is 1/6

Hence, for A and B, rate is 1/2

From 9:00 a.m. when the inlets are turned on till 10:30 a.m.

1/2 x 3/2 = 3/4

i.e. 3/4th of the cistern is full.


However, I am unable to proceed from this point onwards. Can you please assist? Thanks for your help.

Regards,
Sri

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Hi Sri,

This question is not properly worded, but the "intent" of this question is that the "outlet" drains water out.

You've correctly deduced that the two inlets will completely fill the cistern at a rate of 1/2 per hour (thus, the cistern will be filled in 2 hours). The outlet removes water at such a rate that at 10:30am, it takes a full hour to fill the cistern (as opposed to the 1/2 hour that it would take if there was no outlet at all).

So, at 10:30am, the cistern is 3/4 full, but then the outlet is turned on and it starts draining water....an hour later, the cistern is full. Since the cistern will be 1/2 full after an hour, the outlet must be removing 1/4 of the tank during that time (3/4 + 1/2 - 1/4 = 1 = full).

Thus, the outlet removes 1/4 of the water in 1 hour.

The question asks how long it will take the outlet to empty the cistern when it's full. Since the outlet removes 1/4 of the water in 1 hour, it will remove the entire volume of water in 4 hours.

GMAT assassins aren't born, they're made,
Rich

[Tushar14]

The time taken by the two inlets to fill the cistern. This comes out to be (6*3)/(6+3) = 2 hours. With the outlet open for one hour, the inlets take 2.5 hours to fill the cistern. This means
Volume of water flowing through the outlet in 1 hr = Volume of water flowing in through both the inlets in 0.5 hrs
=> Vol of water flowing through the outlet in 1 hr = 0.5 (1/3 + 1/6) = 1/4 of the capacity of the cistern
=> Time taken to empty the cistern by the outlet working alone = 4 hours.

[GMATGuruNY]

There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?

(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours

Let the cistern = 12 gallons.

Since the faster inlet takes 3 hours to fill the cistern, the rate for the faster inlet = w/t = 12/3 = 4 gallons per hour.
Since the slower inlet takes twice as long -- 6 hours -- to fill the cistern, the rate for the slower inlet = w/t = 12/6 = 2 gallons per hour.
Combined rate for the two inlets = 4+2 = 6 gallons per hour.

In the 1.5 hours from 9am to 10:30am, the amount of fluid pumped IN by the two cisterns = r*t = (6)(3/2) = 9 gallons.
Remaining fluid to be pumped in = 12-9 = 3 gallons.
Since the cistern is filled after 1 more hour, the rate for the final hour = 3 gallons per hour.

The oultet decreases the hourly rate from 6 gallons per hour to 3 gallons per hour.
Implication:
The outlet's rate = 3 gallons per hour.
Thus:
Time for the outlet to empty the cistern = w/r = 12/3 = 4 hours.

The correct answer is E.

[gmattesttaker2]

Hi Sri,

This question is not properly worded, but the "intent" of this question is that the "outlet" drains water out.

You've correctly deduced that the two inlets will completely fill the cistern at a rate of 1/2 per hour (thus, the cistern will be filled in 2 hours). The outlet removes water at such a rate that at 10:30am, it takes a full hour to fill the cistern (as opposed to the 1/2 hour that it would take if there was no outlet at all).

So, at 10:30am, the cistern is 3/4 full, but then the outlet is turned on and it starts draining water....an hour later, the cistern is full. Since the cistern will be 1/2 full after an hour, the outlet must be removing 1/4 of the tank during that time (3/4 + 1/2 - 1/4 = 1 = full).

Thus, the outlet removes 1/4 of the water in 1 hour.

The question asks how long it will take the outlet to empty the cistern when it's full. Since the outlet removes 1/4 of the water in 1 hour, it will remove the entire volume of water in 4 hours.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Thanks for the excellent explanation.

Best Regards,
Sri