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Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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29 Apr 2010, 11:40

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Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

A) 42 minutes B) 14 minutes C) 39 minutes D) 40 minutes 20 seconds E) None of these

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Last edited by Engr2012 on 17 Aug 2015, 16:10, edited 2 times in total.

Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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29 Apr 2010, 12:24

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aiming4mba wrote:

Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

In one cycle they fill 40+30-20 = 50 liters

700 = 50*n => n = 14 here n = number of cycles.

total time = 14*3 = 42 as in one cycle there are 3 minutes.

thus 42 minutes....whats the OA?
_________________

Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

In three minutes net gain is 40+30-20=50 liters;

After 13 cycles (13*3=39 minutes) net gain will be 13*50=650 liters.

Then in 1 minute pipe A will add 40 liters, 10 liters to be filled;

Then to fill 10 liters pipe B will need 10/30=1/3 min.

So total time \(39+1+\frac{1}{3}=40\frac{1}{3}\) min.
_________________

Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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29 Apr 2010, 12:38

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Bunuel wrote:

aiming4mba wrote:

Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

In three minutes net gain is 40+30-20=50 liter;

After 13 cycles (13*3=39 minutes) they fill 13*50=650 liters.

Then in 1 minute pipe A will add 40 liters, 10 liters to be filled;

Then to fill 10 liters pipe B will need 10/30=1/3 min.

So total time \(39+1+\frac{1}{3}=40\frac{1}{3}\) min.

Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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06 Jul 2010, 06:34

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@ bibha

divide 700/50... u get 14 cycles. but u know that before 20 then take away the last cycle. so u have 13 cycles (39 mins), where the tank is 650 ls full. let's take the 14th cycle. the first minute, the tank gets to 650 + 40 = 690ls. there's only 10 ls left to fill the tank. the second step of the cycle is pipe B that fills 30 ls in 1 minute. since we only need 10 ls, we only need 1/3rd of a minute.

so we have 13 cycles plus 1 min of pipe A and 1/3rd minute of pipe B.
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Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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07 Jun 2013, 06:17

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I still dont get it.... i mean I understand everything but the logic as to why we should NOT consider 14 cycles as we have already done the filling in and filling out calculations.

Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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07 Jun 2013, 06:28

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samheeta wrote:

I still dont get it.... i mean I understand everything but the logic as to why we should NOT consider 14 cycles as we have already done the filling in and filling out calculations.

The sequence of the events is: Pipe A adds \(40\) liters/m Pipe B adds \(30\) liters/m Pipe C subtracts \(20\) liters/m =NET \(+50\)

When you have done 13 circles in 40 minutes, there are 650 liters and 50 to go. Now the squence repeats Pipe A adds \(40\) liters/m----50-40=10 liters to go and 1 minute more added Pipe B adds \(30\) liters/m----so 10 liters will be filled in \(\frac{1}{3}\) of a minute STOP Pipe C subtracts 20 liters/m

Tot time \(40\) minutes and \(\frac{1}{3}\)
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Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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20 Nov 2013, 10:53

aiming4mba wrote:

Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

tricky tricky! I had gotten 42 minutes at first, not realizing it would actually finish at 700, but also hit 700 before, 1/3 of the way into B's cycle on the 20th go around.

Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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17 Aug 2015, 04:35

Bunuel wrote:

aiming4mba wrote:

Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?

In three minutes net gain is 40+30-20=50 liters;

After 13 cycles (13*3=39 minutes) net gain will be 13*50=650 liters.

Then in 1 minute pipe A will add 40 liters, 10 liters to be filled;

Then to fill 10 liters pipe B will need 10/30=1/3 min.

So total time \(39+1+\frac{1}{3}=40\frac{1}{3}\) min.

Bunuel, It's very tricky.. why we can't use "14*50=700" equation.
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Re: Pipe A fills a tank of capacity 700 liters at the rate of 40 [#permalink]

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17 Aug 2015, 04:59

Engr2012 wrote:

ImHURT wrote:

Bunuel, It's very tricky.. why we can't use "14*50=700" equation.

Do you mind explaning a bit more where are you getting this "14*50=700" equation from?

As above Bunuel used 13 cycles of 50 Litres to fill the tank to its capacity of 650 litres. I just added one more to 13 i.e, 14*50=700 litres. As full capacity of the tank is 700 litres. I want to ask why we stopped at 13 cycles. Sorry, if it is a silly question to ask.
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Bunuel, It's very tricky.. why we can't use "14*50=700" equation.

Do you mind explaning a bit more where are you getting this "14*50=700" equation from?

As above Bunuel used 13 cycles of 50 Litres to fill the tank to its capacity of 650 litres. I just added one more to 13 i.e, 14*50=700 litres. As full capacity of the tank is 700 litres. I want to ask why we stopped at 13 cycles. Sorry if it is a silly question to ask.

Good question.

As mentioned by Bunuel, if we have 13 cycles (with 1 cycle = A for 1 minute + B for 1 minutes - C for 1 minute), we will have filled 650 out of 700 litres.

After this, for the next minute (39+1)th minute, A will add another 40, leading to 650+40=690 litres and then B will have added another 10/30 litres in 1/3 of a minute. So technically we dont need the entire 14th cycle as we have reached the capacity fo 700 litres. If you keep B on for any longer than 1/3rd of a minute, the water will start to overflow from the tank.

If you go the entire 14 cycles, the water would have overflowed by the time entire of B was done and with C draining water after B was done, there would be less water than 700 litres. This is the reason why we did not do 14*50=700. This is a classical trap in GMAT.

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