Question

QUESTION: 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.

Answer 1

||✪✪ GIVEN ✪✪||

• output increase same every year.
• In last two years output is doubled ..

|| ✰✰ ANSWER ✰✰ ||

Let The initital Output was X . (Before Two year).

And, Let Each Year it increases by Y% ..

It is given That , now, In last two years output is doubled .. So, Output become = 2 * X = 2X .

A/q,

→ X[ 1 + (y/100)]² = 2X

Dividing both sides by X,

→ [ 1 + (y/100)]² = 2

Square - Root Both sides now,

→ [ 1 + (y/100)] = √2

Putting value of √2 as 1.4142 now ,

→ [ 1 + (y/100)] = 1.4142

→ (y/100) = 1.4142 - 1

→ (y/100) = 0.4142

→ y = 100 * 0.4142

→ y = 41.42% .

Hence, The Required % which increase Every year is 41.42% .

Answer 2

Answer:

=> 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 ans.