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Operating at a constant rate, 2 pumps of Type 1 can completely fill a

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Operating at a constant rate, 2 pumps of Type 1 can completely fill a  [#permalink]

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New post 26 Nov 2017, 13:17
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Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water?

A) 1 AM on 22 March
B) 7 AM on 22 March
C) 1 AM on 23 March
D) 7 AM on 23 March
E) 7 AM on 25 March

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Re: Operating at a constant rate, 2 pumps of Type 1 can completely fill a  [#permalink]

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New post 26 Nov 2017, 18:22
vitorcbarbieri wrote:
Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water?

A) 1 AM on 22 March
B) 7 AM on 22 March
C) 1 AM on 23 March
D) 7 AM on 23 March
E) 7 AM on 25 March


We know the rate of type 1, so let's work on it.
2 type I fill in 24 hrs, so 6 will fill in 24*2/6=8..
Now these 6 type I pumps work from 3 to 7 pm, so 4hrs
In 4 hrs, these pump will finish 4/8=1/2 work..

So remaining half work is done by 3 type II pumps in 7-1=6hrs..
So these 3 would have filled the reservoir in 6*2=12 hrs..
12 hrs after 1pm on 21 march means 1am on 22 march.

A
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Re: Operating at a constant rate, 2 pumps of Type 1 can completely fill a  [#permalink]

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New post 27 Nov 2017, 05:30
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vitorcbarbieri wrote:
Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water?

A) 1 AM on 22 March
B) 7 AM on 22 March
C) 1 AM on 23 March
D) 7 AM on 23 March
E) 7 AM on 25 March


Type 1 :
2 pumps can fill a reservoir in 24 hours.
So, 1 pump can fill reservoir in 48 hours.
In 1 hour 1 pump can fill 1/48th of reservoir.

Type 2 :
Let 1 pump of type 2 can fill a reservoir in x hours.
So, in 1 hour 1 pump of type 2 can fill 1/x th of reservoir.

At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM.
So, 3 pumps of type 2 is running for 6 hours and 6 pumps of type 1 is running for 4 hours.
Hence, 3*1/x*6 + 6*1/48*4 = 1
18/x +1/2 =1
x = 36.

So, 1 pump of type 2 can fill a reservoir in 36 hours.
If 6 pumps of Type 1 were not started. Only 3 pumps of type 2 had to fill the reservoir.

Time taken = 36/3 = 12 hours
So, reservoir would have been filled at 1 AM on 22nd march.

Answer A

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Re: Operating at a constant rate, 2 pumps of Type 1 can completely fill a &nbs [#permalink] 27 Nov 2017, 05:30
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