### Author Topic: PIPES AND CISTERNS  (Read 4225 times)

#### Mohd Liyaqat Hussain

• Newbie
• Posts: 6
##### PIPES AND CISTERNS
« on: February 09, 2014, 11:16:35 AM »

Daniel sir ,
i have a doubt in pipes and cisterns topic like if already the tank is filled some volume...
see i'am writing the question below...

Q):A water tank is two-fifth full. pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?
a)6min. to empty
b)6min. to fill
c)9min. to empty
d)9min. to fill

• Daniel
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• Posts: 18
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##### Re: PIPES AND CISTERNS
« Reply #1 on: February 10, 2014, 09:15:16 AM »
Ok so this is how you solve it

If pipe A fills the tank in 10 mins, means every minute it fills (1/10)th of the tank
If pipe B empties the tank in 6 mins, means every minute it empties (1/6)th of the tank

So if both the pipes are on, the net work done every minute is (1/10) - (1/6) = (6-10)/60 = -4/60 = -1/15

So now -1/15 is getting emptied every min that the two pipes are open

Consider this : Your tank is 2/5 full   Since its a fraction, we can multiply the same number in the numerator and denominator without changing the value right ?

Multiply 3 on top and below
So (2 X 3)/(5 X 3) = 6/15

So now since the part of the tank with water is 6/15 and the net work of pipes A & B is -1/15 ......

The pipes will empty the tank in 6 mins

Hence the correct answer is (a) 6 min to empty

Math is Beautiful Its like poetry
If Math doesn't give you your expected answer, then don't Blame Math.
Math is NEVER wrong You are

#### Mohd Liyaqat Hussain

• Newbie
• Posts: 6
##### Re: PIPES AND CISTERNS
« Reply #2 on: February 10, 2014, 09:51:43 AM »
thanks