Pipes and Tanks problems, shortcuts and tricks, formulas, examples.

Pipes and Tanks Problems :
Pipes and Tanks Problems
1) One tap fills one tank in 10 hours, another tap fills that tank in 20 hours, how long will it take to fill the tank if both taps are started simultaneously.
Ans. :
Time to fill the tank = ( 10 × 20 ) / ( 10 + 20 )
Time to fill the tank = 200 / 30
                                     = 20 / 3
                                     = 6.66 hours.
So it will take 3.66 hours to fill the tank.

2) One tap fills one tank in 10 hours, another tap fills that tank in 15 hours, how long will it take to fill the tank if both taps are started simultaneously.
Ans. :
Time to fill the tank = ( 10 × 15 ) / ( 10 + 15)
Time to fill the tank = 150 / 25
                                     = 6 hours.
So it will take 6 hours to fill the tank.

3) One tap fills one tank in 10 hours and the other tap empties the tank in 20 hours. How long will it take to fill the tank if both taps are started at the same time?
Ans. :
Here,
Time to fill the tank = ( 10 × 20 ) / ( 20 - 10 )
Time to fill the tank = 200 / 10
                                     = 20 hours.
Note : subtract denominator because one tap filling the tank and other is emptying the tank.

4) One tap fills one tank in 6 hours and the other tap empties the tank in 8 hours. How long will it take to fill the tank if both taps are started at the same time?
Ans. :
Here,
Time to fill the tank = ( 6 × 8 ) / ( 8 - 6)
Time to fill the tank = 48 / 2
                                     = 24 hours.
5) One tap fills one tank in 10 hours, another fills in 20 hours and a third fills in 30 hours how long will it take to fill the tank if all three taps are started at once?
Ans. :
a =  10        b = 20          c = 30
 Time to fill the tank = abc / ( ab + bc + ac )
                                      = ( 10 × 20 × 30 ) / { ( 10 × 20 ) + ( 20 × 30 ) + ( 10 × 30 ) }
Time to fill the tank = 6000 / ( 200 + 600 + 300 )
                                    = 6000 / 1100
                                    = 60 / 11
Time to fill the tank = 5. 45 hours.

6) Two taps fill a tank in 12 minutes and 16 minutes. When both taps are started at once, the other tap should be closed after how long the tank will fill in 9 minutes.
Ans. :
a =  12          b = 16       t = 9
How long after the second tap to turn off = b { 1 - ( t / a ) }
= 16 { 1 - ( 9 / 12 ) }
= 16 { 1 - ( 3 / 4 ) }
= 16 × ( 1 / 4 )
= 4 minutes.
Therefore, when the second tap is turned off after 4 minutes, the tank will fill up in 9 minutes.

7) Three taps A, B and C fill the tank in 60 minutes. When tap C is closed after 10 minutes, A and B taps fill the tank in 80 minutes. So how long will it take to fill the C tank alone?
Ans. :
a =  60         b = 80        t = 10
A single C tap will fill the tank =
 { ab / ( b - a  + t ) }
= { 60 × 80 / ( 80 - 60 + 10 ) }
= 4800 / 30
= 160 minutes.
So a single tap C will fill the tank in 160 minutes

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