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# In 2008, a certain factory produced 25% more widgets than it did in 20

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In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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18 Apr 2017, 05:09
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In 2008, a certain factory produced 25% more widgets than it did in 2007. In 2009 the company’s production of widgets was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?

A. 33%
B. 45%
C. 50%
D. 64%
E. 67%

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In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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Updated on: 18 Apr 2017, 07:15
Lets say, we had 200 widgets produced in 2007.
In 2008, there was a 25% increase. The number of widgets produced became 250.
Next year there was a 20% increase in the production
(since the number of widgets was 120% of its production last year)
20% of 250 is 50, which means 300 widgets were produced in 2009.

In 2010, we need the same widgets as in 2007(200)
200 is apprx 66.67% of 300, which is the total production of widgets in 2009.
Hence, we need a 33.3% decrease (Option A)
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Originally posted by pushpitkc on 18 Apr 2017, 06:18.
Last edited by pushpitkc on 18 Apr 2017, 07:15, edited 2 times in total.
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In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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Updated on: 18 Apr 2017, 09:08
Total widgets in 2007, lets say, was 100. 2008 saw a 25% increase in production...2008 total was 125. In 2009, production was at 120%...2009 total was 150. (100-150)/150 = 33%
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Originally posted by emockus on 18 Apr 2017, 06:51.
Last edited by emockus on 18 Apr 2017, 09:08, edited 1 time in total.
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In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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Updated on: 18 Apr 2017, 16:32
By default, I took it as a raise.. its correct for the 125%, hence option A. Need to check in detail. Thanks
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Originally posted by umadurga on 18 Apr 2017, 07:02.
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Re: In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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18 Apr 2017, 07:41
I believe the answer is 33% (A).

Lets consider, Production in 2007= 100
In 2008= 1.25* 100= 125
In 2009= 1.2 *125= 150 ( It says 120% times of 2008 production, not increased by 120%)

So percent difference to match with 2007 production
= (150-100)/150
= 33% (Approx.)

*Correct me if wrong*
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Re: In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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18 Apr 2017, 22:13
Bunuel wrote:
In 2008, a certain factory produced 25% more widgets than it did in 2007. In 2009 the company’s production of widgets was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?

A. 33%
B. 45%
C. 50%
D. 64%
E. 67%

Here is my approach

Let's say x is the production in 2007 and y is the production decrease percent

x*(125/100)*(120/100)*(y/100)=x
(15/10)*(y/100)=1
y=1*1000/15
y=66.66667% Aprox. 67%

Please correct me if I'm wrong.

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Re: In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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19 Apr 2017, 10:28
Amolpi wrote:
I believe the answer is 33% (A).

Lets consider, Production in 2007= 100
In 2008= 1.25* 100= 125
In 2009= 1.2 *125= 150 ( It says 120% times of 2008 production, not increased by 120%)

So percent difference to match with 2007 production
= (150-100)/150
= 33% (Approx.)

*Correct me if wrong*

Shouldn't it be
(150-50)/150 = 67% (approx)?
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Re: In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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19 Apr 2017, 10:33
Here's what I did:

2007 widgets = x

2009 Widgets = x * 1.25 * 1.20 = 1.5x

Change to 2007 widgets = (x - 1.5x)/1.5x * 100 = 66.67% = 67% approx.

Please let me know if you see an error.
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In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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24 Apr 2017, 16:19
Bunuel wrote:
In 2008, a certain factory produced 25% more widgets than it did in 2007. In 2009 the company’s production of widgets was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?

A. 33%
B. 45%
C. 50%
D. 64%
E. 67%

Useful property: percent increase and percent decrease are inversely proportional . . .
That means we can just flip a fraction. STEPS:

1) find the multiplier for the percent increase;
2) convert that to a fraction;
3) flip that fraction;
4) if we need a percent decrease, subtract that fraction from 1

That fraction's percent value is the percent decrease needed.

Let the factory's production = Q

1) Q increases twice: 2007-08 = 1.25, and 2008-09 = 1.2

To find Q's total percent increase, multiply the multipliers:

Total percent increase: $$1.2 * 1.25 = 1.5$$

2) Convert to a fraction:

$$1.5 = \frac{150}{100}=\frac{3}{2}$$

3) Flip that fraction, to $$\frac{2}{3}$$

4) Subtract from 1*: $$(1-\frac{2}{3})=\frac{1}{3}$$

PERCENT DECREASE NEEDED: $$\frac{1}{3}\approx{33}$$%

*By flipping the fraction, we determine that the old Q is $$\frac{2}{3}$$ of the current Q.
To get from (current) 1 Q to $$\frac{2}{3}$$ Q (old), subtract $$\frac{1}{3}$$ Q = 33%.
OR: $$\frac{2}{3}$$ is 67%, which is 33% less than 100%

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Re: In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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12 Jun 2017, 22:32
Bunuel wrote:
In 2008, a certain factory produced 25% more widgets than it did in 2007. In 2009 the company’s production of widgets was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?

A. 33%
B. 45%
C. 50%
D. 64%
E. 67%

x= 2007
x(1.25) = 2008
x(1.25)(1.2)= 2009 * important thing to remember X of y does NOT equal x increased by y

x(1.25)(1.2) (y/100) = x

80= 2007
100= 2008
120 = 2009

120 (y/100) =80
120y = 8000
y= 8000/120
y= 67 ... (doesnt matter what remainder is just round up)

100-y =
100-67 = 33 approximately

Thus A
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Re: In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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01 May 2018, 10:21
Bunuel wrote:
In 2008, a certain factory produced 25% more widgets than it did in 2007. In 2009 the company’s production of widgets was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?

A. 33%
B. 45%
C. 50%
D. 64%
E. 67%

We can let the number of widgets produced in 2007 be 100. Thus the number of widgets produced in 2008 is 100 x 1.25 = 125, and the number of widgets produced in 2009 is 125 x 1.2 = 150. To bring 150 back to 100, we need to decrease the production by:

(150 - 100)/150 x 100 = 50/150 x 100 = 1/3 x 100 = 33 ⅓ percent

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In 2008, a certain factory produced 25% more widgets than it did in 20  [#permalink]

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16 Feb 2019, 01:07
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Bunuel wrote:
In 2008, a certain factory produced 25% more widgets than it did in 2007. In 2009 the company’s production of widgets was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?

A. 33%
B. 45%
C. 50%
D. 64%
E. 67%

------2007------2008-----2009
------100--------125-------150

Now this increase = 150-100/150 * 100

= 33.3

This means that 33% of reduction has to be made to the following year for the factory to produce the same number of widgets it did in 2007
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In 2008, a certain factory produced 25% more widgets than it did in 20   [#permalink] 16 Feb 2019, 01:07
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