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

Question

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%

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

pushpitkc · Answer

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)

emockus · Answer

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%

umadurga · Answer

By default, I took it as a raise.. its correct for the 125%, hence option A. Need to check in detail. Thanks

Amolpi · Answer

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*

maxbm10 · Answer

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%

So the answer is E

Please correct me if I'm wrong.

Regards.

skysailor · Answer

Shouldn't it be 
(150-50)/150 = 67% (approx)?

skysailor · Answer

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.

generis · Answer

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} %

Answer A

*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%

Nunuboy1994 · Answer

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

100-y = answer

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

JeffTargetTestPrep · Answer

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

Answer: A

KanishkM · Answer

------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

Ankur17000 · Answer

Initial Production - X
2008 - 5/4X
2009 - (5/4)(6/5)X=1.5X

Going by word translation:

By what % ---> y/100
Production needed to be decreased(2009 to 2007) --> 1.5X 
2007 ---> X

so 1.5X  = X
Y = 33.33

Answer is A

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

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