Aptitude - Area - Discussion

How? Explain the answer please.

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%.

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.

Please explain the last step of the solution.

The formula X + Y + (X * Y/100) is the best for square and rectangle.

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%

In order to find the percentage error, the formula is [ (x*x) /100+2*x]%.

Exactly @Harsh.

The method is wrong!

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

Percentage error = X+Y+(XY)/100.

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

= 4.04.

Note : This method valid for only two values.

@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.