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.
Answers
||✰✪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 %
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}
41.42%