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In a certain task, a person has to fill an empty tank using four taps

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EgmatQuantExpert
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In a certain task, a person has to fill an empty tank using four taps [#permalink] New post   13 Feb 2019, 06:15
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In a certain task, a person has to fill an empty tank using four taps, each of which can fill the entire empty tank in 1 hour, and once the tank is filled completely, he needs to empty the tank using two outlets, at the bottom of the tank. Both the outlets can empty the full tank in same time. How much time does an outlet take to empty a full tank, if the total time taken by the person to finish the task is 30 minutes?

    A. 1/4 hour
    B. 1/3 hour
    C. 1/2 hour
    D. 3/4 hour
    E. 1 hour


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Re: In a certain task, a person has to fill an empty tank using four taps [#permalink] New post   13 Feb 2019, 06:22
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Time taken by 1 tap to fill tank= 1 hour.
So,time taken to fill the tank when all 4 taps are open= 1/4 hours= 15 minutes.

Since total time taken by the person=30 minutes,
This means that the tank is emptied in 30-15 minutes= 15 minutes.

Now,since 2 taps have equal work rate to empty the tank,this means that the 2 taps took 15 minutes,
Thus,one tap took 30 minutes to empty the tank= 1/2 hours.

Hence,C

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Re: In a certain task, a person has to fill an empty tank using four taps [#permalink] New post   13 Feb 2019, 22:14
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1 tap can fill a tank in 1 hour, then 4 taps can fille the tank in \(\frac{1}{4}\) hour

i.e, 4 taps fill the tank in 15 minutes. Now the entire task of filling the tank and emptying the tank is completed in 30 minutes. So in 30 minutes, the first 15 minutes were to fill the tank and the rest 15 minutes were to empty the tank.

So 2 taps took 15 minutes to empty the tank, then each tap takes 30 minutes to empty the tank.

30 minutes = \(\frac{1}{2}\) hour

OPTION: C
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Re: In a certain task, a person has to fill an empty tank using four taps [#permalink] New post   13 Feb 2019, 22:26
Option: C
time taken for filling => 60 mins/4 = 15 mins (since all taps fill at equal rate)
Total activity time (time to fill + time to empty tank) = 30 mins
therefore, Time taken to empty tank by 2 outlets = 30 - 15 = 15 mins
Since outlets empty at equal rate, time needed by each outlet to empty tank = 15x2 = 30 mins
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Re: In a certain task, a person has to fill an empty tank using four taps [#permalink] New post   14 Feb 2019, 22:40
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Solution



Given:
In this question, we are given
    • In a certain task, a person has to fill an empty tank using four taps, each of which can fill the entire empty tank in 1 hour.
    • Once the tank is filled completely, he needs to empty the tank using two outlets, at the bottom of the tank.
    • Both the outlets can empty the full tank in same time.
    • The total time taken by the person to finish the task is 30 minutes.

To find:
We need to determine
    • The amount of time does an outlet tap take to empty a full tank.

Approach and Working:
As each inlet tap can fill the tank in 1 hour, while 4 taps are working together, the tap will be filled in \(\frac{1}{4}\) hour = 15 minutes
    • Hence, in (30 – 15) = 15 minutes the two outlet taps can empty the tank.
    • As both outlet taps can empty the tank at the same time, each of them individually can empty the tank in 15 x 2 = 30 minutes or \(\frac{1}{2}\) hour.

Hence the correct answer is Option C.

Answer: C


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In a certain task, a person has to fill an empty tank using four taps [#permalink] New post   12 Oct 2023, 00:42
I approached the problem this way.. plz let me know my mistake:

Rate of all 4 fill taps = 1/4
Rate of 2 drain taps = 2/x

Total work = 1 and time taken = 30/60 so, rate = 1/ (30/60) —> 60/30

1/4 - 2/x = 2

-2/x = 2-1/4


-2/x = 7/4

X=-8/7 —> rate of 1 drain tap —> time taken for 2 = 7/8 * 2 = 14/8 = 1.75 h

What am I doing wrongly here ? EgmatQuantExpert
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In a certain task, a person has to fill an empty tank using four taps [#permalink]
12 Oct 2023, 00:42
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