A factory kept increasing its output by the same percentage every year. The percentage if it is know

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25 Feb 2013 Problem

A factory kept increasing its output by the same percentage every year. The percentage if it is known that the output is doubled in the last two years will be

OPtion

1) 34.5
2) 40
3) 41.4
4) 45
5) 49.6
6) 50
7) 49
8) 51
9) 20
10) none of these

Solution

let principle = x
and y is the multiple increment every year
so after 2 year amount = x*y*y = 2x (given)
so y^2 = 2
so y = sqrt(2)
so % = 1.414(100)-100 = 41.4

Correct Option: 3 Best Solution (22)

Dimple   11 years AGO

If p is the earlier production and x % is 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

Like? Yes (8) | No (3)  

sumit jindal   11 years AGO

let output be y 2 years ago and x be the percentage increase. after first year output=y+yx/100
after second year
output=(y+yx/100)+(y+yx/100)*x/100=2y
solving
we get a quadratic eq. in x which gives x=41.4

Like? Yes (8) | No (4)  

Tijo Jose   11 years AGO

Let p be the initial output.
Given, the output increases by some percentage every year, and that the output after two years is 2p.

So, p*(1+x)^2 = 2p
or, (1+x)^2 = 2
Solving, we get x = sqrt(2) - 1 = 0.414 = 41.4%

Like? Yes (6) | No (3)  

krishnapriya   11 years AGO

x(1+r/100)(1+r/100)=2x
1+r/100=sqrt(2)
r/100=sqrt(2)-1=1.4142-1=0.4142
r=0.4142*100=41.42

Like? Yes (3) | No (1)  

AVINASH KUMAR   11 years AGO

let the initial investment is P
then according to question
2P=P(1+R/100)^2
1+R/100=1.414
R/100=.414
R=41.4

Like? Yes (3) | No (2)  

Kalpesh   11 years AGO

Let r be the increase in the rate percent per annum
Let x be the principal
x(1+r/100)2 = 2x
(1+r/100)2 = 2
(1+r/100) = sqrt{2} sqrt{2} = 1.4142
r/100 = 1.4142-1
r/100 = 0.4142
r = 0.4142*100
r = 41.42

Like? Yes (3) | No (2)  

Dr.Dipin Singh   11 years AGO

root 2=1.414

so the factory should keep increasing its output to 1.414 times every year or by 41.4 percent every year so that output is doubled in 2 years..

Like? Yes (4) | No (4)  

Sasmita Ojha   11 years AGO

let the output be x and rate of increase be r
given => x(1+r/100)^2=2x
=>(1+r/100)^2=2
=>r=41.4% (appr)

Like? Yes (2) | No (2)  

shadab siddiqui   11 years AGO

Amt =p(1+R/100)^n
2p=p(1+R/100)^2
R=41.4 %

Like? Yes (3) | No (3)  

Ankit Pandey   11 years AGO

Using growth and depreciation formula,
Output=Input(1+r/100)^n
=>2x=x(1+r/100)^2
=>2^1/2=(1+r/100)
=>1.414*100=100+r
r=41.4%

Like? Yes (3) | No (3)  

Anurag Arora   11 years AGO

let output(o1) = 100
let it increase by x%
new output(o2) = (100 + x)/100 * 100 = 100 + x
in 2nd year = (100 + x + x)/100 * (100 + x)
=> (100 + 2x)(100 + x)/100

Like? Yes (2) | No (3)  

Rats   11 years AGO

((100+R)/100)^2=2
R=41.4

Like? Yes (2) | No (3)  

Mukesh Kr Singh   11 years AGO

let x be principal amount
and r be the rate of interest
then
x(1+r/100)^2=2x
r=41.42

Like? Yes (2) | No (3)  

phani   11 years AGO

let it be 100 before 2 years.then it will be doubled now...100*2=200

100*x/100*x/100=200====>>>>x=100*2^1/2=141.4
so 41.4% increase

Like? Yes (1) | No (2)  

Muhammad Nadeem Haider Naseem   11 years AGO

Let r be the increase in the rate percent per annum
Let x be the principal
According to the given information

Like? Yes (1) | No (2)  

ArunKumar   11 years AGO

Increasing o/p % = x
o/p = x( 1+r/100)^ 2 = 2x
( 1+r/100)^ 2 = 2
r = (sqrt(2) -1 )100
r = 41.42%

Like? Yes (2) | No (3)  

neha priyanka   11 years AGO

1st yr output=x+(y/100 of x)
2nd yr ouput=(x+xy/100)+y/100(x+xy/100)=2x
(x+xy/100)(1+y/100)=2x
x(1+y/100)^2=2x
thus y=41.4

Like? Yes (2) | No (3)  

Vinod Kumar   11 years AGO

proble is seems to be same as compound interest formula

Like? Yes (1) | No (2)  

Abhijeet Kumar   11 years AGO

let x be the initial output of the factory and it increases by y percent each year.After 2 years x becomes 2x.
x(1+y/100)^2 = 2x
=>(1+y/100)^2 = 2
=>(1+y/100) = 1.414
=> y/100 = 1.414-1.000=0.414
=> y = 41.4
Ans is option 3

Like? Yes (2) | No (3)  

srivadan   11 years AGO

p(1+r/100)2=2p
=>(1+r/100)2=2
=>1+r/100=sqrt2
=>1+r/100=1.414
=>r/100=0.414
=>r=41.4
r=41.4%

Like? Yes (1) | No (3)  

sc mandota   11 years AGO

solution is 41.4

Like? Yes (1) | No (3)  

Basani Manoj kumar   11 years AGO

41.4

Like? Yes (1) | No (3)