Question

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

Answer 1

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

Answer 2

let the out put of factory =p
let the percentage of income =x
t=2
a=2p
by A.T.Q
a=p (1+x/100)^2
2p=p (1+x/100 )^2
2p/p=(1+x/100)^2
2=(1+x/100)^2
1+x/100=root2
100+x/100=1.414
100+x=141. 4
x=141. 4
x=41.4percent