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# M05-09

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Math Expert
Joined: 02 Sep 2009
Posts: 46167

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16 Sep 2014, 00:24
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Difficulty:

25% (medium)

Question Stats:

71% (01:46) correct 29% (01:23) wrong based on 136 sessions

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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

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Math Expert
Joined: 02 Sep 2009
Posts: 46167

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16 Sep 2014, 00:24
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Official Solution:

Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

The tank is full in 12 hours, therefore, the effective inflow has to be $$\frac{54}{12} = 4.5$$ liters per hour. Currently our nominal inflow is 12 liters per hour and outflow is unknown. To find the outflow, we need to subtract effective inflow from the nominal inflow. $$12 - 4.5 = 7.5$$; We know that each of the large, outgoing pipes has a flow rate of 1.5 liters per hour, therefore, $$\frac{7.5}{1.5} = 5$$.

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Joined: 09 Feb 2015
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15 May 2015, 02:04
2
Other solutions:
Let x be large pipes:
=> (1*12 - 1.5*x)*12 = 54
Solving we get x=5.
Is it right!
Intern
Joined: 29 May 2015
Posts: 12

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25 Aug 2015, 22:17
If I may elaborate above explanation,

A = RT
54 = Final R * T
54 = (Inflow Rate - Outflow Rate) * T
54 = (12-1.5x)*12
x=5
Senior Manager
Joined: 25 Mar 2013
Posts: 267
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

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03 Feb 2017, 09:10
Empowergmat Rich, can you pls explain this simpliest way to solve this problem
What concept am I lacking to think like Bunuel.
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I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Intern
Joined: 19 Jun 2017
Posts: 11

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11 Sep 2017, 19:33
I think this is a poor-quality question and I agree with explanation. Question should explicitly note that the outflow rate of 1.5 l/h is "in each large pipe" (to borrow from the language of the preceding sentence).

Otherwise, Q is excellent as always. But the answer wouldn't make sense if one didn't assume 1.5l/h was on a per pipe basis (of course, one would eventually figure it out, but I don't think question wording should be allowed to unnecessarily cost the user time).
M05-09   [#permalink] 11 Sep 2017, 19:33
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# M05-09

Moderators: chetan2u, Bunuel

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