BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

pipes and cisterns

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 227
Joined: Sun Apr 08, 2012 4:53 am
Thanked: 12 times
Followed by:3 members

pipes and cisterns

by guerrero » Thu Nov 08, 2012 3:09 pm
Hi All ,

Pipes A and B can fill a cistern in 20 and 30 minutes and C can empty it in 15 minutes. If the three are opened and closed one after the other successively for 1 min. each in that order, how soon will the cistern be filled ?

1)180 min
2)160 min
3)167 min
4)187 min


I could calculate part filled in 3 mins = 1/60th Part .

part filled in 177 min = 59/60th

remaining part = 1- 59/60 = i/60

i am stuck after this step . Please help me understand the approach .

thanks in advance !
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Nov 08, 2012 7:52 pm
guerrero wrote:Hi All ,

Pipes A and B can fill a cistern in 20 and 30 minutes and C can empty it in 15 minutes. If the three are opened and closed one after the other successively for 1 min. each in that order, how soon will the cistern be filled ?

1)180 min
2)160 min
3)167 min
4)187 min


I could calculate part filled in 3 mins = 1/60th Part .

part filled in 177 min = 59/60th

remaining part = 1- 59/60 = i/60

i am stuck after this step . Please help me understand the approach .

thanks in advance !
Let the cistern = 60 units.

A's rate = 60/20 = 3 units per minute.
B's rate = 60/30 = 2 units per minute.
C's rate = 60/15 = -4 units per minute.
When the pipes work in succession, their combined rate for each three-minute cycle = A+B-C = 3+2-4 = 1 unit per cycle.

From here, we can plug in the answers, which represent the time needed to fill the cistern.

Answer choice B: 160 minutes
160/3 = 53 R1.
Here, there will be 53 three-minute cycles (during which all 3 pipes operate in succession) plus 1 extra minute (during which only pipe A operates).
Total number of units filled = 53 + 3 = 56.
Since 60 units are needed to fill the cistern, eliminate B.

Answer choice C: 167
167/3 = 55 R2.
Here, there will be 55 three-minute cycles (during which all 3 pipes operate in succession) plus 2 extra minutes (during which only pipes A and B operate in succession).
Total number of units filled = 55 + 3 + 2 = 60.
Success!

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Master | Next Rank: 500 Posts
Posts: 227
Joined: Sun Apr 08, 2012 4:53 am
Thanked: 12 times
Followed by:3 members

by guerrero » Fri Nov 09, 2012 2:19 am
thank you so much , Mitch . Nice approach . Now i get the confidence back :)
Top
Post new topic Post Reply
• Page 1 of 1