# Three Pipes Attached to a Tank

Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?

#### smilewithabc Profile Answers by smilewithabc

• Mar 1st, 2010

For Every 3 minutes volume of water filled ---  1/20 + 1/30 -1/15 = 1/60

So for 3 minutes 1 part will be filled out of 60 parts.

Total to Fill full tank is 3 * 60  = 180 mins = 3hours

#### saritha1406 Profile Answers by saritha1406

• Oct 13th, 2010

The part of tank filled by Pipe A in 1 min = 1/20
The part of tank filled by Pipe B in 1 min = 1/30
The part of tank emptied by Pipe C in 1 min = 1/15
The part of tank filled in 1 min is 1/20 + 1/30 - 1/15 = 1/60

The total time taken to fill the tank is 60 min = 1 hr.

#### chris

• May 25th, 2012

you can not fill the tank while pipe c is still opened.. a & b is for storage and pipe C is for draining..

#### Manoj K L

• Aug 19th, 2016

The part of tank filled by Pipe A in 1 min = 1/20
The part of tank filled by Pipe B in 1 min = 1/30
The part of tank emptied by Pipe C in 1 min = 1/15
So totally in 3 minute (because open for 1 minute each)=1/20+1/30-1/15=1/60.
so consider 55/60 can be filled in 3*55=165min,remaining part is 1/12.
A can fill in 1 min is 1/20,so in 1min A can fill (1/12-1/20) so finally left is 1/30 so B can fill remaining 1/30 in 1 Minute
So total time taken=(3*55+1+1)=167min. So within 167min it can fill the tank.(fastest way)

#### Manaswini

• Nov 21st, 2016

Please explain why you have taken 55/60.

• Jan 12th, 2017

The part of tank filled by Pipe A in 1 min = 1/20
The part of tank filled by Pipe B in 1 min = 1/30
The part of tank emptied by Pipe C in 1 min = 1/15
So totally in 3 minute (because open for 1 minute each)=1/20+1/30-1/15=1/60.
so consider 55/60 can be filled in 3*55=165min. As 165th min is over, C is turned off. At 166th minute, A is turned on. A fills 1/20 per minute.
Therefore,
166th minute = 55/60 + 1/20 = 58/60th is filled.
B fills 1/30 per minute
167th minute = 58/60 + 1/30 = 1=Full.
Therefore, 167 minutes.

#### hiren mistry

• Feb 28th, 2017

Where is that 55 coming from?

#### gagan

• May 19th, 2017

167 minutes

#### Aazam khan

• Jul 12th, 2017

Ans is 167
For those getting confused why 55?
Its because total work is 60 units.
3 pipes work successively.So for 1st 3 minutes only 1unit per min work is done (3unit/min+2unit/min-4unit/min)
Now for the second minute work done/min is also 1unit/min but as we know in the first minute the pipe already did 1unit per minute.So the combined work in 2nd minute is 1+1 i.e 2unit/min
Similary for 3rd minute its 3unit/min
4th min its 4unit/min.
.
.
.
.
9th min its 9unit/min
10th min its 10 unit/min
For 11th min......wait before that let me chech the total work done in these 10 minutes.
It will be 1+2+3+4+5+6+7+8+9+10=55
If we take 11th minutr also the work done will be 66unit.But we know total work is 60unit only
So time taken to do 50unit in 3min/unit is 155
Remaining is 5 units which will be filled by A and B im next 2minutes
Ans is 167 minutes

#### Ratan

• Sep 4th, 2017

Why should we add those units?

#### rahul

• Dec 7th, 2017

A and B can fill the tank as 1/20+1/30=5/60 for 2 mins
C an empty it as -1/15 i.e, -4/60in 1 min
Now together they will fill 5/60-4/60=1/60 for 3 mins
So at the end of 55th successive (to match with the last iteration avoiding Cs intervention in last iteration) iterations the tank is filled as 55/60 for 55X3 mins=165 mins
now when A and B are opened for the next two mins then the amount filled is 5/60 with the already filled amount of 55/60 which gives 1 that means that the tank is filled
thus the total time is
time for reaching 55/60+time for which A and B were open
=165+2=167 mins  