Word problem

[mia.eigo]

Need your help in understanding the following problem (source: majortests.com):

A circular logo is enlarged to fid the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?

A 50
B 80
C 100
D 125
E 250

Explanation: If the diameter of the old lid is 100, the diameter of the new lid is 150. This gives a ratio of 2:3

The areas of the lids will be in the ration 2^2: 3^2 or 4:9

This represents an increase in area of 5 units for every 4 units. 5/4 is equivalent to 125%. The answer is D



What I can't understand is why the areas of the lids are2^2: 3^2? I used the general formula of two pi r square, but got the wrong answer. Thank you.

[gbd97]

We know the formula of area of circle is,
A=pi r^2
as Pi is constant, A is proportional to r^2
In this way their formula works. Even if you do by using the general formula, this is correct.
There is a shortcut formula for this types of math.

If radius of a circle increases by x% then the area will increase
by : 2x+ x^2/100
In this case x=50, so area increased=2*50+50^2/100=125

[mia.eigo]

I got it! Thanks!

[tommywallach]

Hey Guys,

Actually, the best way to do a question like this is not to try to be all genius-y with the theory. I mean, it's great if you can do that, but I definitely wouldn't do it that way. I'd just say:

r = 2
area = pi * r ^ 2 = 4pi

r = 3 (an increase of 50%)
area = pi * r^2 = 9 pi

9pi/4pi = 9/4 = 225%

That's an increase of 125% (because we start at 100%).

Way easier than trying to figure out the theory! : )

-t