Aptitude - Area - Discussion

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%.

Suppose,

The Original Length of one side is 10m, Then area for this is 100m² &
Length when 2% error is excess is 10+0.2, it means now the length of a side is 10.2m and the area for this is 104.04m².
Now,
The area due to error excess - Original area = 104.04 - 100.
= 4.04.
Also, we can assume the length of a side is 100m or whatever we want.

Here, it is mentioned that the error excess of 2% so for that reason we add the value of the error on the original side instead of subtracting.

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.

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.

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.

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%

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.

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%.

@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.

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)