QUESTION: A factory kept increasing its output by the same percentage

1.	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» \|\|✰✪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. \|\|✪✪ 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 $\sf\fbox{41.42}$ %

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»

||✰✪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.

||✪✪ 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 $\sf\fbox{41.42}$ %