# Aptitude - Area - Discussion

### Discussion :: Area - General Questions (Q.No.2)

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%

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.

 Dwaipayan said: (May 26, 2019) You are right, Thanks @Harsh.

 Tejasri Samala said: (Aug 28, 2019) In order to find the percentage error, the formula is [ (x*x) /100+2*x]%.

 Rohith said: (Nov 28, 2019) We can also solve this is in 404/10.

 Harshavardhan Reddy said: (Dec 19, 2019) Use the formula {A+B+(AB/100)}. Here A=2 for side. For area A=B. 2+2+2*2/100=4.04.