An outlet pipe empties a tank which is full in 10 hours. If

Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 8*60 = 480 liters/hour;
Net outflow rate when both pipes operate would be x-480 liters/hour.

Capacity of the tank = x*10 hours = (x-480)*(10+6) hours

10x=(x-480)*16 --> x=1280 --> capacity = 10x = 12800 liters.

Answer: C.
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Hi,

Time to empty the tank with outlet pipe open = 10 hrs
Time when both inlet and outlet is open =10+6 = 16

So time went up by 60% or is 8/5 of original time. So outflow of water is down by 5/8

Let rate of outlet pipe = x

So new flow is 5/8 of original flow

5x/8 = x - 8

solve this x = 64/3

So volume = 64/3*10*60 = 12800 L

Rate at which the outlet pipe pumps out water: x Ltr in 10 hours: (x/600) Ltr/min
Rate at which the inlet pipe pumps in water: 8 Ltr/min

Rate at which the tank will be emptied when both inlet and outlet pipe are openend: x Ltr in 16 hours: (x/960) Ltr/min

Outlet rate - Inlet rate = Net outlet rate
(x/600) - 8 = (x/960)

Solving the equation gives x=12800L. Hence C.

outlet pipe worked for extra 6hrs, so it emptied \(\frac{6}{10}\) tank extra.
this \(\frac{3}{5}\) tank must be filled by inlet pipe.
total liters filled by inlet pipe in 10+6hrs = 8*60*16 liters

let capacity of tank = \(x\)
\(\frac{3*x}{5} = 8*60*16\)
\(x = \frac{5*8*60*16}{3}\)

\(x = 12800\)

HTH

I solved it in a different way.

rate of water flow in outlet pipe = \(1/10\)
rate of water flow in inlet pipe = \(1/x\)
1/10 - 1/x = 1/(10+6)

1/x =\(6/160\)

Therefore, in 1 hr 6/160th of the capacity of the tank is let in = 8*60 =480 litres
therefore the complete capacity = \(480\) * \(160 /6\) = 12800

Let the tank's capacity be 'x' liters
Outlet's rate: x/10 l/h
Inlet's rate: 8 l/min= 480 l/h

Outlet takes 16 hours to empty the full tank when inlet is on.

In 16 hours; inlet would have filled: 16*480 = 7680 liters of water

Thus, Outlet pipe empties a total volume of "x+7680" at a rate of x/10 l/h in 16 hours.

R * t = W
(x/10) * 16 = x+7680
16x = 10x+76800
6x=76800
x=76800/6=12800 litres

Ans: "3"

There are various ways of approaching this problem. Given below is my take.

Whatever water the inlet pipe pumps-in in 16 hrs, outlet pipe pumps out in 6 hrs (since it takes 6 hrs longer when inlet pipe is open for 16 hrs)
If output pipe were to pump out the water in 10 hrs, inlet pump needed to pump in for 16*10/6 = 80/3 hrs
In 80/3 hrs, inlet pipe would pump in 8*60*80/3 = 12800 lts of water (since inlet pipe pumps in at the rate of 8 liters/min or 8*60 liters/hr)
Answer (C)
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v/10 - outlet rate

Inlet rate = 480L/hr

v/10 - 480 = v/16

v( 8-5)/80 = 480 => v = 480 * 80/3 = 16 * 8 * 100

So the answer is C.
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If it empties the tank in 10 hours it does 1/10 per hour
Now with the inlet pipe open it will take 16 hours, hence in one hour it does 1/16

So the difference is 1/10 - 1/16 = 3/80 work done per hour

Now, we are told that the inlet pipe lets water in at the rate of 8 litres/min or 480 litres per hour

Hence 3/80x = 480

x = 12800

Hence answer is C

Hope it helps
Cheers!
J

Let the capacity = C

Total vol of water came out of outlet valve in 16hrs = Initial Vol (i.e. C) + Water added through inlet valve (8 l/min) in 16hrs.

C/10 X 16 = C + 480X16

C = 12800

Let the capacity of the tank = x

Time ...................... Rate .......................... Capacity

10 ........................... \(\frac{x}{10}\) ............................ x (This is for outgoing water to empty the tank)

Inlet pipe rate = 8 lts/min = 480 Lts/hr


\(\frac{x}{480}\) .......................... 480 ........................... x (Time required for Inlet pipe is x/480)

Total water going out of pipe = Water in tank + Water from inlet pipe

\(\frac{x}{10} (10+6) = x + 480 * (10+6)\)

x = 12800

Answer = C

so basically, the pipe needs 6 hours to remove the additional water.
the total additional water is 8l/min * 60 = 480 liters/hour. 16 hours = 480x16.

now, this will be removed in 6 hours..this can only mean that 480x16=6/10 of the total capacity of the tank.
total capacity of the tank = 480x16x10/6 = 12,800 liters
was thinking of backsolving...but it would have taken much more time..

The first sentance has modifier issues, that led me to wrong direction and I wasted 30 mints to figure out pretty much noting. I hope not to see such questions again.
Is it just me or someone alse had this problem too?

Supposing that the inlet pipe takes x hours to fill the empty tank, then (1/10) - (1/x) = 1/16
Solving we get x = 80/3 hours.
Therefore, the capacity of the tank is 80/3 * 60* 8 = 12800 liters.

An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.

A. 8600 litres
B. 200 litres
C. 12800 litres
D. 11200 litres
E. 13200 litres


let c=tank's capacity
if outlet pipe empties 1 tank in 10 hours,
then it will empty 1.6 tanks in 16 hours
thus, inlet pipe must fill .6 tank in 16 hours
.6*c=16*60*8 litres
c=12800 litres
C

We can let the capacity of the tank = x liters.

Since it takes 10 hours for the pipe to empty the tank, the rate of the outlet pump is x/10 litres/hour.

The rate of the inlet pipe is 8 litres/min, or 8 x 60 = 480 litres/hour.

However, if the inlet pipe were left open, then it would take 16 hours to empty the tank.

Using the work formula, work = rate x time, we see that the work of the outlet pipe is (x/10)(16) = 16x/10 = 8x/5 and the work of the inlet pipe is (480)(16) = 7680.

We see that there are two actions working against each other: the inlet pipe is letting water in, but the outlet pipe is letting water out. The net amount of work done (emptying the tank of x litres of water) is the difference in these two actions. We can create the following equation to determine x:

8x/5 - 7680 = x

Multiplying the entire equation by 5, we have:

8x - 38,400 = 5x

3x = 38,400

x = 12,800

Answer: C
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I HAVE DONE THIS QUESTION IN ANOTHER WAY HOPE YOU ALL FIND THIS EASY

Let the Capacity of the tank be 'x' Liters

Thus according to the question
'x' Liters is drained out in 10 Hours
And when Inlet pipe adds 8 L/min it takes 16 Hours for the Outlet pipe to empty the same tank

Therefore Amount of water added by the inlet pipe in 1 Hours is 8 L/min * 60 min = 480 L/hr
As the outlet pipe took 16 Hours to empty the tank so the Inlet pipe must also be running for 16 Hours
Amount of water added by Inlet pipe in 16 Hours = 16 * 480 Liters = 7680 Liters

Thus,
10 Hours to Empty 'x' Liters
16 Hours to empty 'x'+7680 Liters

By Cross Multiplying
10 * (x+7680) = 16x

By solving we get 'x' = 12,800 Liters which is the capacity of the tank as asked by the Question.

Outlet works 6 hours in excess of 10 hours becasue the inlet pipe was filling tank for 16 hours.

i.e. Inlet work of 16 hours = Outlet work of 6 hours
i.e. 16*60*8 = (6/10)*Tank
i.e. Tank = 12800 Lt

Answer: Option C
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let capacity of tank be x liters
so at first outlet pipe rate = x/10
later 8lpm i.e. 480 lph
and outlet time = 16 hrs or say rate = x/16
we get
x/16-480 = x/10
solve for x
x-7680= 8x/5
x = 12800 ltrs
option C