M4maths Previous Puzzles

05 May 2017 Area

An error 3% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

OPtion

1) 4.04 %
2) 4.14 %
3) 5.25 %
4) 5.00 %
5) 5.75 %
6) 6.00 %
7) 6.09 %
8) 6.25 %
9) 9%
10) None of these

Solution

Lets assume side is 100 cm
100 cm is read as 103 cm.

A1 = (100 x 100) cm2 and A2 = (103 x 103) cm2.

Difference in Area:
(A2^2 - A1^2) = [(103)2 - (100)2]
= (103 + 100) x (103 - 100)
= 203*3
= 609

Percentage error = (609x100)/(100*100) = 6.09%

Correct Option: 7 Best Solution (11)

Mukund Manohar   7 years AGO

Let the correct value of side of square = 100
Measured Value = 100 + 3 = 103
Corrected area of square = 100*100 = 10000
Calculated area of square = 103 *103 = 10609
Error = 10609 - 10000 = 609
Percentage Error = (609/10000)*100 = 6.09%

Like? Yes (4) | No (1)  

Amarnath Kumar Upadhyay   7 years AGO

Area of square without error A1=100^2
Area of square with error A2=103^2
percentage error=(A2-A1/A1)*100
103^2-102^2/100^2=6.09%
Ans 6.09%

Like? Yes (1) | No   

Parveen Soni   7 years AGO

let x be side of square
then area is x^2
now
error in excess means x is measured as x+x*3%=1.03x
and then area will be 1.0609x^2
so error % will be (1.0609-1)*100===>
0.0609*100=6.09% error in area

Like? Yes (1) | No   

Devendra Marghade   7 years AGO

Let side of a square is x, its area is x^2.
When side is increased by 3%, new length=1.03x and area=1.03x*1.03x=1.0609x^2
So percentage error=100(1.0609x^2 - x^2)/x^2=6.09
Option 7)

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SUBHAM KUMAR ARYA   7 years AGO

error in side of square=3%
let side be 100 unit.
new side=103 unit
area of square=103*103=10609.
% error=[(10609-10000)*100]/10000=6.09%ans

Like? Yes | No   

Haritha Mummidivarapu   7 years AGO

let side of a square be 100cm, => area = 10000 sq.cm
with 3% error the side becomes 103cm, => area= 10609 sq.cm
so , error in area = 10609 - 10000 = 609
% error = 609*100/10000 = 6.09%

Like? Yes | No   

Azim Uddin Siddiqui   7 years AGO

Let original length of square be X units, so area will b X^2.
Due to 3% error each side now is 1.03x & area is 1.0609x^2. so increase in area is .0609 i.e. 6.09%

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g lokesh   7 years AGO

Let's take side of the square is 100 cm
now the error is 3% , side is 103 cm
% of error=103*103*100/100*100
= 106.09
% is 6.09

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Vahira Bollina   7 years AGO

100 cm read as 103cm

A1= (100*100)cm^2
A2=(103*103)cm^2

A2-A1=(103^2 - 100^2)
= (103+100)(103-100)
=609cm^2
percentage error= (609/(100*100) * 100)%
=6.09%

Like? Yes | No   

mcamanjeet   7 years AGO

(((103)^2 - (100)^2)/(100*100))*100
=(((103+100)*3)/(100*100))*100
=6.09%

Like? Yes | No   

G.S.Kantharao   7 years AGO

Let the measure is 100
Actual measure is 100
Difference of Areas .=(103^2-100^2=609
Percentage of difference=(609{/10000)*100=6.09
Hence the right option is 7.

Like? Yes | No