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When n liters of fuel was added to a tank that was already

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When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Apr 2012, 05:55
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When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n
B. 4/3 n
C. 3/2 n
D. 9/4 n
E. 7/3n
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Apr 2012, 07:03
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naveenhv wrote:
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n
B. 4/3 n
C. 3/2 n
D. 9/4 n
E. 7/3n


Say the capacity of the tank is 9 liters;

So, there are already 3 liters (1/3*9=3) of fuel and after adding n liters there are 7 liters (7/9*9=7) --> 3+n=7 --> n=4 --> capacity=9=n*9/4.

Or just plug n=4 in the answer choices to see which option yields 9, answer choice D fits: 9/4*4=9.

Answer: D.
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Re: Fractions  [#permalink]

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New post 20 Apr 2012, 06:06
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D is the answer.

To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.

Given
- tank was already 1/3 full.
- When n ltr added, it became 7/9

So 1/3 + n = 7/9
n = 7/9 - 3/9
n = 4/9

capacity of the tank is full fraction . i.e. 1 i.e. 9/9

so the question is 9/9 is how much times n
= 9/9 = 1 = xn

so x = 9/4

and total = 9/4n
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Apr 2012, 07:15
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Or you can also solve it another way, check for the integer, which is divisible by both the fractions, here we can take 18 liters as the capacity of the tank.

Then 1/3 of fuel is 6 liters, and 7/9 capacity will be 14 liters. From this we can get the n value as n = 14-6 = 8.
Try to substitute this value in the below options and only option 'D' get the value of 18 as the total capacity.
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Apr 2012, 07:19
mission2009 wrote:
Or you can also solve it another way, check for the integer, which is divisible by both the fractions, here we can take 18 liters as the capacity of the tank.

Then 1/3 of fuel is 6 liters, and 7/9 capacity will be 14 liters. From this we can get the n value as n = 14-6 = 8.
Try to substitute this value in the below options and only option 'D' get the value of 18 as the total capacity.


The lowest value for the capacity for which 1/3*capacity and 7/9*capacity are integers is 9 (LCM of 3 and 9). Refer to the solution above.
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Jul 2016, 12:14
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Here are a couple of video explanations for this question.

Algebra:



Value Substitution:

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When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Jul 2016, 14:08
let capacity=9/9
9/9-3/9-2/9=4/9=n
(9/9)/(4/9)=9/4
capacity=9/4 n
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 08 Jan 2017, 10:27
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What if :
7/9-1-3 = n
=>, 4/9 capacity = n
so full capacity = 9n/4
Ans. D
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 20 Feb 2017, 17:15
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Also, we can answer it this way,

1/3*c+n=7/9*c
c/3+n=7c/9
n=7c/9-c/3
n=4c/9

The question asked is what is the capacity of the tank, in liters? so here as we have already considered C as the capacity of the tank.
C=9/4*n which is the option D.
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 26 Jan 2019, 14:39
naveenhv wrote:
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n
B. 4/3 n
C. 3/2 n
D. 9/4 n
E. 7/3n


N liters added to a tank 1/3 full, equals 7/9 of its capacity, which translates to:

n + 1/3c = 7/9c
n + 3/9c = 7/9c
n = 7/9c - 3/9c
n = 4/9c

To make in terms of n, multiple both sides by 9/4.
c = 9/4n

Answer is D
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Re: When n liters of fuel was added to a tank that was already  [#permalink]

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New post 26 Jan 2019, 14:44
naveenhv wrote:
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n
B. 4/3 n
C. 3/2 n
D. 9/4 n
E. 7/3n


When you see variables in the answer choices, use smart numbers.

Suppose that the capacity of the tank is 27 liters. (I chose 27 because it's divisible by the other numbers in the problem). In that case, the tank already contained 9 liters, and when we added a certain amount, it was filled to 7/9(27), or 21 liters. That means n = 21-9 = 12.

So, n = 12, and the capacity is 27. Try plugging 12 into the answer choices, and see whether you end up with 27.

(A) 10/9(12) isn't an integer!
(B) 4/3(12) = 16 - too small
(C) 3/2(12) = 18 - too small
(D) 9/4(12) = 27 - perfect!
(E) 7/3(12) = 28 - too big
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Re: When n liters of fuel was added to a tank that was already   [#permalink] 26 Jan 2019, 14:44
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