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# The denominator of a fraction is 5 greater than the numerator. If the

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Math Expert
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The denominator of a fraction is 5 greater than the numerator. If the  [#permalink]

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31 Jan 2016, 07:06
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15% (low)

Question Stats:

78% (01:12) correct 22% (01:42) wrong based on 78 sessions

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The denominator of a fraction is 5 greater than the numerator. If the numerator and the denominator are increased by 2, the resulting fraction is equal to 7⁄12. What is the value of the original fraction?

A. 5⁄12
B. 1⁄2
C. 9⁄14
D. 2⁄3
E. 12⁄17

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Re: The denominator of a fraction is 5 greater than the numerator. If the  [#permalink]

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31 Jan 2016, 11:55
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Let the original fraction be x/(x+5)
If the numerator and the denominator are increased by 2, the resulting fraction is equal to 7⁄12.
(x+2)/(x+7) = 7/12
=> 12x + 24 = 7x + 49
=> 5x = 25
=> x =5
Original fraction = 5/10 = 1/2
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Re: The denominator of a fraction is 5 greater than the numerator. If the  [#permalink]

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02 Feb 2016, 22:42
Hi All,

This math behind this question can be dealt with in a couple of ways. Depending on how the answer choices appear, the actual amount of work involved can be quite minimal though.

We're told that the denominator of a fraction is 5 greater than the numerator and that when the numerator AND the denominator are increased by 2, the resulting fraction is equal to 7⁄12. We're asked for the value of the original fraction.

Let's work backwards from the last piece of information: increasing the numerator and denominator by 2 gives us a fraction that equals 7/12. Since that fraction MIGHT be reduced, we could end up having to 'check' several iterations (7/12, 14/24, 21/36, etc.)

If we start with 7/12 and SUBTRACT 2 from both the numerator and the denominator, we end up with (7-2)/(12-2) = 5/10 = 1/2. Since that answer appears among the 5 choices, we're done.

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Re: The denominator of a fraction is 5 greater than the numerator. If the  [#permalink]

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03 Feb 2016, 00:28
Bunuel wrote:
The denominator of a fraction is 5 greater than the numerator. If the numerator and the denominator are increased by 2, the resulting fraction is equal to 7⁄12. What is the value of the original fraction?

A. 5⁄12
B. 1⁄2
C. 9⁄14
D. 2⁄3
E. 12⁄17

Let, Fraction = a / (a+5)

New Fraction i.e. (a+2) / (a+5+2) = 7/12

i.e. (a+2) / (a+7) = 7/12

12a + 24 = 7a + 49
i.e. a = 5

Original Fraction = 5/(5+5) = 5/10 = 1/2

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Re: The denominator of a fraction is 5 greater than the numerator. If the  [#permalink]

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27 Aug 2018, 06:40
Bunuel wrote:
The denominator of a fraction is 5 greater than the numerator. If the numerator and the denominator are increased by 2, the resulting fraction is equal to 7⁄12. What is the value of the original fraction?

A. 5⁄12
B. 1⁄2
C. 9⁄14
D. 2⁄3
E. 12⁄17

$$\frac{n}{n + 5}$$

If the numerator and the denominator are increased by 2 then we have -

$$\frac{n + 2}{n + 5 + 2} = \frac{7}{12}$$

Or, $$\frac{n + 2}{n + 7} = \frac{7}{12}$$

So, $$n = 5$$

Hence the original fraction must be $$\frac{5}{5 + 5} = \frac{5}{10} = \frac{1}{2}$$, Answer must be (B)

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Re: The denominator of a fraction is 5 greater than the numerator. If the &nbs [#permalink] 27 Aug 2018, 06:40
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