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# After 4,000 gallons of water were added to a large water tan

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Math Expert
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After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 00:55
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then at 4/5 of its capacity. How many gallons of water does the tank hold when filled to capacity?

(A) 5,000
(B) 6,200
(C) 20,000
(D) 40,000
(E) 80,000

Problem Solving
Question: 61
Category: Algebra First-degree equations
Page: 69
Difficulty: 600

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 00:55
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SOLUTION

After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then at 4/5 of its capacity. How many gallons of water does the tank hold when filled to capacity?

(A) 5,000
(B) 6,200
(C) 20,000
(D) 40,000
(E) 80,000

4,000 gallons of water comprise 4/5 - 3/4 = 1/20, which makes the capacity of the tank equal to 4,000*20 = 80,000 gallons.

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 01:32
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Initially the tank is 75% full.

and 4000 gallons are added. then the tank becomes 4/5 or 80% full.

so 5% is 4000. Then the 100% will be

= $$4000 *100/5= 80,000$$.

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 02:26
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We can set up the following equation for the info in the question:

3/4 of x+4000=4/5 of x; where x is the capacity of the water tank.

x=80,000

We can alternatively work this out using proportion: we know that the additional 4000 gallons account for 4/5-3/4=1/20 of the tank. So if 4000 gallons account for 1/20 of the full tank, then 20/20 of the tank is 80,000.

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 07:54
1
1/20x=4000..x=80000..
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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 11:12
1
x=tank capacity

4000/x = (4/5-3/4)/1
4000 = 1/20(x)
x=80000

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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28 Jan 2014, 20:41
1
Let us assume the total capacity of tank to be x.

Since the tank was already filled to 3/4th(or 75%) of its capacity and 4,000 gallons of water were added to bring it to 4/5 th(or 80%) of its capacity, we can make the following inference:
5% of capacity(80%-75%) = 4000;
(5/100) * x = 4,000
x = 80,000;

Ans is (E).
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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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01 Feb 2014, 06:51
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SOLUTION

After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then at 4/5 of its capacity. How many gallons of water does the tank hold when filled to capacity?

(A) 5,000
(B) 6,200
(C) 20,000
(D) 40,000
(E) 80,000

4,000 gallons of water comprise 4/5 - 3/4 = 1/20, which makes the capacity of the tank equal to 4,000*20 = 80,000 gallons.

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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11 Jul 2014, 00:07
1
Let full capacity of tank = x

3/4th of full capacity $$= \frac{3x}{4}$$

Addition of 4000 gallons $$= \frac{3x}{4} + 4000$$

Given that addition of water takes the level to 4/5th

$$\frac{3x}{4} + 4000 = \frac{4x}{5}$$

x = 4000 * 20

= 80000
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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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29 Jul 2016, 11:00
1
Nice Question
Here making an algebraic equation => [3/4] X +4000 = [4/5]X => X=80000
Smash E
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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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23 Sep 2018, 02:32
1
3/4*x+4000=4/5*x
Solving for x, and getting x = 80K
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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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02 Feb 2014, 05:48
After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then at 4/5 of its capacity. How many gallons of water does the tank hold when filled to capacity?

(A) 5,000
(B) 6,200
(C) 20,000
(D) 40,000
(E) 80,000

$$\frac{3}{4}$$ of Tank = 75% of Tank

$$\frac{4}{5}$$ of Tank = 80% of Tank

Given that, difference between 80% and 75% of Tank is 4000 gallons
Or, 5% of Tank = 4000 gallons

Or, Full capacity of Tank $$= 20 * 4000 = 80000$$ gallons of water

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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11 Jul 2014, 04:54
Let x be the capacity of tank

(4/5 - 3/4) x = 4000
(0.8-0.75)x = 4000
0.05 x = 4000
x = 4000 * 20 = 80,000
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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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19 Oct 2018, 04:12
Let the currently existing water be x
Total capacity be y

$$\frac{x}{y} = \frac{3}{4}$$

$$\frac{x+4000}{y} = \frac{4}{5}$$

$$\frac{x}{y} + \frac{4000}{y} = \frac{4}{5}$$

$$\frac{3}{4} + \frac{4000}{y} = \frac{4}{5}$$

$$\frac{4000}{y} = \frac{1}{20}$$

y = 80,000

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Re: After 4,000 gallons of water were added to a large water tan  [#permalink]

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09 Jan 2020, 21:44
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Re: After 4,000 gallons of water were added to a large water tan   [#permalink] 09 Jan 2020, 21:44
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