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# Arithmetic Aptitude :: Pipes & Cistern

Home > Arithmetic Aptitude > Pipes & Cistern > General Questions

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11. Bucket A has thrice the capacity as bucket B. It takes 80 turns for bucket A to fill the empty drum. How many turns it will take for both the buckets A and B, having each turn together to fill the empty drum?

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Explanation:

Lets Assume capacity of bucket A = x
so capacity of bucket B = x/3

Given that it takes 80 turns for bucket A to fill the empty drum.
So capacity of the drum = 80x

Number of turns required if both A and B having each turn together=80x/(x+x/3)=240x/(3x+x)=60

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12. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

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Explanation:

Tank part filled by pipe A in 1 minute = 1/60
Tank part filled by pipe B in 1 minute =1/40

So Tank Part filled by both pipes A and B in 1 minute = (1/60+1/40)=5/120=1/24

Lets Assume tanker get filled in x minutes.
Then, to fill the tanker from empty state, B is used for x/2 minutes
and A and B together is used for the rest x/2 minutes.

(x/2*1/40)+(x/2*1/24)=1
=> x/2(1/40+1/24)=1
=> x/2*8/120=1
=> x/30=1
=> x = 30 minutes

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13. Pipe A can fill an empty tank in 12 hours. Pipe B can empty it in 36 hours. If at 8 a.m. the pipe A is opened on an empty water tank and pipe B is opended at 9 a.m., 10 a.m. 11 a.m. and 12 p.m. for 15 minutes each, by what time in the evening will the tank be filled?

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Explanation:

Tank part filled by Pipe A in 1 hour = 1/12
similarly Tank part emptied by pipe B in 1 hour = 1/36
or Tank part emptied by pipe B in 15 min = 15 * 1/60*36 = 1/144

From 8 a.m. to 9 a.m. tank part filled = 1/12 => 11/12 of the tank is empty
From 9 a.m. to 10 a.m. tank part will be filled = (1/12 + 1/144) = 11/144 => 1 hour 11/144 of the tank gets filled
11/12 part of the tank would take = 11/12 x 144/11 = 12 hours
Total time required is 1 + 12 = 13 hours
=> Tank would be full @ 8 a.m. + 13 = 9 p.m.

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14. Three taps A,B and C can fill a tank in 12,15 and 20 hours respectively. If A is open all the time and B ,C are open for one hour each alternatively, the tank will be full in:

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Explanation:

Tank filled by (A+B) in 1 hour = (1/12+1/15) = 9/60 = 3/20
Tank filled by (A+C) in 1 hour = (1/12+1/20) = 8/60 = 2/15
So tank filled in 2 hours = (3/20 + 2/15) = 17/60
Tank part filled in 6 hrs = 3*17/60 = 17/20

Remaining part = (1-17/20) = 3/20

Now, it is the turn of A and B (3/20) part is filled by A and B in 1 hour.
So Total time taken to fill the tank =(6+1)hrs= 7 hrs

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15. There are 2 taps A and B to fill up a water tank. The tank can be filled in 40 minutes if both taps are on. The same tank can be filled in 60 minutes if tap A alone is on. How much time will tap B alone take to fill up the same tank ?

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Explanation:

Tank part filled by (A+B) in 1 min = 1/40
Tank part filled by A alone in 1 min = 1/60
=> Tank part filled by B alone in 1 min = (1/40 -1/60) = 1/120
Therefore Tap B can fill the tank in 120 minutes

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16. 8 taps through which water flows at the same rate can fill a tank in 30 minutes. If two taps go out of order, how long will the remaining taps take to the fill the tank?

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Explanation:

Given Time need by 8 taps to fill tank = 30 minutes
So let's assume time need by 6 taps to fill tank = M minutes
M = (8 x 30)/6 = 40 minutes

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17. 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?

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Explanation:

Pipe B is faster than pipe A
=> the tank will be emptied.
part to be emptied = 2/5
Tank part emptied by (A+B) in 1 minute= (1/6-1/10)=1/15
1/15:2/5::1:x =>2/5 = 1/15x=> x = 6min
so, the tank will be emptied in 6 min

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18. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

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Explanation:

Tank part filled by pipe A in 1 min = 1/20
similarly by pipe B in 1 min = 1/24

So Work done by waste pipe in 1 min = 1/15 - (1/20+1/24) = -1/40(Here negative value means emptying)
Volume of 1/40 part = 3 gallons
Volume of whole = 3*40 = 120 gallons.

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19. Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much more time will it take to fill the tabk by pipe B?

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Explanation:

Tank part filled by pipe A in 1 minute = 1/12
similarly by pipe B = 1/15
Tank part filled by both pipe in 1 min = (1/12+1/15)
so tank part filled by both pipe in 3 min = 3*(1/12+1/15) = 9/20
So remaining part to be filled by B = (1-9/20) = 11/20
1/15 part of tank filed by B = 1 min
so 11/20 part of tank filled by B = 15 * 11/20 = 8 1/4 min.

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20. A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?

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