Question

a factory kepts increasing its output by the same percentage every year find the percentage increase of it is known that the output is doubled in the last 2 years​

Answer 1

Answer:

41.42%

Step-by-step explanation:

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Comparing Quantities

Increase and Decrease in Percentage

A factory kept increasing i...

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Asked on December 26, 2019 bySukhpreet Motwani

A factory kept increasing its output by the same percentage every year. Find the percentage if it is known that the output is doubled in the last two years.

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ANSWER

Let P be the initial production (2 years ago), and let the increase in product every year be x %.

Then, Product at the end of first year =P+100Px=P(1+100x)

Product at the end of the second year

=P(1+100x)+100x{P(1+100x)}=P(1+100x)(1+100x)=P(1+100x)2

Since product is doubled in last two years

∴P(1+100x)2=2P⇒(1+100x

Given that the output is doubled in last two years Let the output before 2 years be x Hence after two years it will be 2x n = 2 Recall the formula,  ∴ R = 41.42%

Answer 2

Step-by-step explanation:

$\huge\fcolorbox{red}{pink}{Answer}$

Let P be the initial production (2 years ago), and let the increase in product every year be x %.

Then, Product at the end of first year =Px100Px

=P(1+100x )

Product at the end of the second year

=P(1+ 100x )+ 100x {P(1+ 100/x)}

=P(1+100x )(1+100x)

=P(1+ 100x ) 2

Since product is doubled in last two years

∴P(1+ 100x )2

=2P⇒(1+100x ) 2 =2

⇒(100+x) 2 =2×100 2

⇒x 2+200x−10000=0

⇒x= 2−200± 200 2 +40000

⇒x=−100±100 2

=100(−1±2 )⇒x=100(−1+2 )=41.42%

OR U CAN WRITE EASILY:

LIKE THIS ONE'S NOT TIME CONSUMING...

if p is the earlier production and x% is the rate of increase in production, then

p*(1+x/100)^2=2p

(1+x/100)^2=2

(1+x/100)=1.414

x/100=0.414

x=41.4

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