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Math Expert V
Joined: 02 Sep 2009
Posts: 56268
If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:40) correct 24% (01:57) wrong based on 57 sessions

### HideShow timer Statistics If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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Bunuel wrote:
If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

Let the original fraction will be $$\frac{x}{y}$$

If the numerator is decreased 25% and the denominator is increased 25%,
the resultant fraction becomes $$\frac{0.75x}{1.25y} = \frac{3}{5}*\frac{x}{y}$$(60% of its original value)

Therefore, the percentage decrease should be 40%(Option A)
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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3064
If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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Bunuel wrote:
If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

Assigning numbers here works well.

Original fraction
Use numbers that yield easy results when multiplied by $$\frac{3}{4}$$ (.75) and $$\frac{5}{4}$$ (1.25)

Let the original fraction = $$\frac{100}{100}$$ (which = 1)

New fraction
The numerator is decreased 25 percent. The denominator increases by 25 percent. New fraction:

$$\frac{75}{125}$$ (which =$$\frac{3}{5}$$)

Percent decrease?
Percent decrease generally:

$$\frac{|New-Old|}{Old}*100$$

Percent decrease here $$\frac{|\frac{3}{5}-1|}{1}*100)=(|-\frac{2}{5}|*100)=(0.4*100)=$$
40 percent decrease

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Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: If the numerator of a fraction is decreased 25 percent and the denomi  [#permalink]

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Bunuel wrote:
If the numerator of a fraction is decreased 25 percent and the denominator of that fraction is increased 25 percent, then the difference between the resulting and the original fractions represents what percentage decrease?

(A) 40%

(B) 45%

(C) 50%

(D) 60%

(E) 75%

We can let the original fraction = n/d and the new fraction = 0.75n/1.25d = (3n/4)/(5d/4) = 12n/20d = 3n/5d

Now we can determine the percent decrease:

[(3n/5d) - (5n/5d)]/(n/d) x 100

-2n/5d x d/n x 100 = -2/5 x 100 = -40, a 40% decrease

Alternate Solution:

Let’s let the original fraction be 1/1. When the numerator is decreased by 25% and the denominator is increased by 25%, the new fraction is 0.75/1.25 = 75/125 = 3/5.

We use the percent change formula (new - old)/old x 100%:

(3/5 -1)/1 x 100% = -2/5 x 100% = -40 percent, which is a 40% decrease.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If the numerator of a fraction is decreased 25 percent and the denomi   [#permalink] 22 Feb 2018, 09:17
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