A factory keeps increasing output of its goods by the same percentage every year. Find the Percentage if it known that the output is doubled in last two years:
1. (-∫2+1 )×100%
2. ( √2+1 ) × 100%
3. ( √2-1 ) × 100%
4. None of these
Answers
Answer:
Percentage = (√2 -1) * 100 %
option 3 is correct
Step-by-step explanation:
A factory keeps increasing output of its goods by the same percentage every year. Find the Percentage if it known that the output is doubled in last two years:
1. (-∫2+1 )×100%
2. ( √2+1 ) × 100%
3. ( √2-1 ) × 100%
4. None of these
Let say factory output in beginning = 10000X
Let say its out put increases by Y %
then output after 1 Year = 10000X + (Y/100)10000X
= 10000X + 100XY
Output after 2nd Year = (output after 1 year ) + Y % increase over that
= 10000X + 100XY + (Y/100)(10000X + 100XY)
= 10000X + 100XY +100XY + XY²
= 10000X + 200XY + XY²
Output is doubled in two years
10000X + 200XY + XY² = 2 * 10000X
=> 200XY + XY² = 10000X
=> 200Y + Y² = 10000
=> Y² + 200Y - 10000 = 0
Y = (-200 + √(40000 + 40000))/2
Y = (-200 + √80000)/2
Y = (-200 + 200√2)/2
Y = -100 + 100√2
Y = (√2 -1) * 100
Percentage = (√2 -1) * 100 %
option 3 is correct
Answer:
Option 3 is correct.....✌️