Aptitude - Area - Discussion

2. 

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

[A]. 2%
[B]. 2.02%
[C]. 4%
[D]. 4.04%

Answer: Option D

Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.

(A2 - A1) = [(102)2 - (100)2]

= (102 + 100) x (102 - 100)

= 404 cm2.

Percentage error = 404 x 100 % = 4.04%
100 x 100


Ramesh said: (Mar 6, 2011)  
Sir Percentage error is not understanding. Please solve the answer.

Sakshi said: (Mar 7, 2011)  
We can also get the percentage by this.

Percentage error = 404/100 = 4.04

Anbu said: (Dec 4, 2011)  
(A2 - A1) = [(102)2 - (100)2] How it come?

Please advise

Amrita said: (Dec 10, 2011)  
To find out error we got to subtract it first.

Shreya Singh said: (Feb 3, 2012)  
In this type of % some usefull idea is to take default no as 100 and in question 2% is error. Hence our no is 100 error no is 102.

So solve further with square formula:

Area= (side)* (side)

Mazher said: (Feb 8, 2012)  
Why we are taking this three 100's ?

Meghna said: (Apr 8, 2012)  
@anbu.
Take the formula a^2-b^2
which is equal to (a+b)(a-b) ... so (102-100)(102+100)

Shikha said: (Apr 29, 2012)  
Why are we dividing 401 by 100 two times and not one time?

Why it is not- (401*100) /100?

Pradyumna said: (Oct 16, 2012)  
@Sikha.

That is (404*100) /(100*100).
Because we are finding the %error.
Where 404 is change in area and (100*100) for original area.

Hasini said: (Sep 24, 2013)  
Correct area = (100)^2.

Measured area = (102)^2.

So to get the excess area we have to subtract the incorrectly measured area by the correct area.

(102)^2-(100)^2.

(102+100)(102-100) .

202*2.

= 404.

So, 404/100.

= 4.4%.

Srikanth said: (Oct 24, 2013)  
Remember this formula x+y+(xy/100).

For rectangle x and y are different, I mean length and breadth are different. Here is square so, only single element we can consider x and y as side of the square.

So (+ for increase and "-" for decrease) 2+2+(2*2/100) = 404/100 = 4.04%.

Lets check an example for rectangle if length increased 5% and breadth decreased 4% so the result is

5-4+(5*(-4))/100 = 0.8% over all decrease.

User said: (Dec 28, 2013)  
@Sreekanth you are right. Thanks for sharing with us. And this seems to be very easy method for solving these kind of problem.

Bhavana said: (May 19, 2014)  
Why are we taking 100 for this sum when it is not mentioned in the question. Please explain?

Aditi said: (Jun 22, 2014)  
Why are we taking 100 for this sum when it is not mentioned in the question. Please explain?

Aarti said: (Jun 30, 2014)  
Solution:

x+y+x*y/100 = 2+2+2*2/100 = 4.04.

Nitin said: (Jul 5, 2014)  
%error = a+b+ab/100.

a and b are +ve and -ve as per increment and decrement respectively.

Lipu said: (Sep 29, 2014)  
Error % = (error/true value)*100.

So (404/100*100)*100 = 4.04

Kasinath @Hyd said: (Oct 7, 2014)  
Correct value is 100*100.
Measured value is 102*102.
Therefore ERROR Value is (102*102)-(100*100) = 404.

Error% = (error value/ true value)*100.

=> (404/100*100)*100 = 4.04.

Engr. Md. Easir Arafat said: (Nov 23, 2014)  
Let's the side to be 1.

Here calculated (1+(2/100)) = 1.02.

Hence the area becomes (1.02*1.02) = 1.0404 but the actual area was supposed to be (1*1) = 1.

The difference = 1.0404-1.00 = 0.0404 = 4.04/100 = 4.04%.

Note: Although taking only two decimals is conventional but in such types of small quantities we should take more to minimize the affect of error as much possible.

Sohel said: (Feb 14, 2015)  
It can be also done as.

Assume side of the square. Let S = 100 excess error is 2% i.e., 102.

Now Area of the Square A = S*S.

A = 100*100 = 10,000 cm2 (with out error) 1.

A = 102-102 = 10,404 cm2 (with 2% excess error) 2.

Difference b/w 1 and 2 is 404.

i.e, 404/100 = 4.04%.

Hope it will help you.

Mahesh said: (Jul 26, 2015)  
Why you all are consider side of the square is 100.

If we are tack original side of the square is 50.

2% error so side is 50*2/100 = 1. So side of square is 51.

= (51)^2 - (50)^2 = (51+50) (51-50) = 101/100 = 1.01 answer.

Please explain me.

Harsh said: (Sep 10, 2015)  
Why is this method wrong?

A = a^2;
dA = 2*a*da;
dA/A = 2*(da/a).

We know da/a = 2%. Hence, dA/A = 4%.

I don't seem to understand the reason why this is wrong? Can someone explain?

Harsh said: (Sep 10, 2015)  
@Mahesh,

Difference in the area is indeed 101 but you must not divide it by 100. The area for your square was 2500 (50*50) and multiplying this by 100 (for percentage) gives you (101/2500)*100 = 4.04.

Abhishek Maurya said: (Jan 10, 2016)  
Percentage error = X+Y+(XY)/100.

So, => 2+2+(2*2)/100.

= 4.04.

Note : This method valid for only two values.

Danah Bader said: (Mar 26, 2016)  
Exactly @Harsh.

The method is wrong!

I don't seem to understand the reason why this is wrong?

Pranjal said: (Apr 20, 2016)  
The formula X + Y + (X*Y/100) is the best for square and rectangle.

Bhavna said: (Aug 4, 2016)  
2% is the excess
Let say area is 100 cm.

Therefore,
Wrong area is 100 + 2 cm.
Right area is 100 cm.

Wrong - Right = (102)^2 - (100)^2.
404.

Error is - (excess/total area) i.e. 404/100 which gives 4.04

Now you can find the percentage by multiplying and dividing by 100.

Ans -> 4.04%

Raju said: (Nov 19, 2016)  
The formula X + Y + (X * Y/100) is the best for square and rectangle.

Sakshi said: (Feb 4, 2017)  
Please explain the last step of the solution.

Arpita said: (Apr 29, 2017)  
But it isn't given that error is made and the length is increased by 2cm.
I mean 2%of 100 = 2.

But then we can even subtract 2 from 100 which us 98 instead of adding that 2.

Please help me.

Shivangi said: (Sep 2, 2017)  
Let the actual side of the square be "a" units.

then Actual area=a*a sq units
2% excess in side=102*a/100 (lets call this side "a1").

Excess Area =a1*a1=(102*a/100)*(102*a/100)
=(2601*a^2)/2500 sq units.

Now, error in area=Excess Area-Actual area
=(2601*a^2)/2500-(a^2) sq units
= (101a^2)/2500 sq units.

Now percentage error=(error in area/actual area)*100
=(((101a^2)/2500)/a^2)*100
=101/25
= 4.04%.

Jobin said: (Apr 10, 2018)  
Percentage error=
( Experimental value - theoretical value )/theoretical value *100.

Therefore,
Here percentage error= [(102)^2 - (100)^2]/(100)^2,
= 404*100/(100)^2.

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