### Author Topic: PIPES AND CISTERN PROB  (Read 5601 times)

#### kumar halijol

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• Posts: 1
##### PIPES AND CISTERN PROB
« on: February 28, 2014, 01:32:20 AM »
Q1. Pipe A takes 16 min to fill a tank. Pipes B and C, whose cross-sectional circumferences are in the ratio 2:3, fill
another tank twice as big as the first. If A has a cross-sectional circumference that is one-third of C, how long will
it take for B and C to fill the second tank? (Assume the rate at which water flows through a unit cross -sectional
area is same for all the three pipes.

plz provide soln this problem

• Daniel
• Newbie
• Posts: 18
• Strive for Open Education & Free Learning! :)
##### Re: PIPES AND CISTERN PROB
« Reply #1 on: March 02, 2014, 12:20:23 AM »
Hey Kumar This is a really good problem Im not really sure if my solution is right But this is what I think

Alright so Pipe A takes 16 min to fill a tank. Now Pipe B and C have cross sectional circumferences in ratios 2:3 .. Circumferences means 2*pi*r  .
However when talking about pipes, we are interested in flow per unit area. Meaning the AREA is important for us. So since we know that
Area = pi*r*r , we will have to square the ratios to get the actual area ratios. Hence in terms of Area, B and C have cross sectional areas in the ratio 4 :9 .

But they've given that A has a one third circumference of C. So the ratio can be 1:3 ...Now combining all these statements we can say that the

Ratios of Circumference of A: B :C = 1 : 2 : 3

AND Ratios of Area of A : B : C = 1 :4 :9

So that means Pipe B fills tank 1,  4 times faster than Pipe A &
Pipe C fills tank 1, 9 times faster than Pipe A.

Now coming to the 2nd tank... we know that Since its twice as big as the first, A will take 32 min to fill this tank right ?

So every min, Pipe A would have to do  (1/32) of the work

But Pipe B and Pipe C will together do the work 13 ( 4 + 9) times faster than Pipe A.

So every minute, Pipe B and C do 13 * ( 1/32) = 13/32 of the work.

So basically if we Invert this by "RULE of FLIP", then we know that Pipe B & C will take (32/13) mins or Just under 2.5 mins to fill the tank together

Once again, Im not really sure of this solution But Im pretty sure this is the way to approach this problem

Hopefully we can discuss this a little further and find whether the solution is right or no
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