Ratio problem : Petersons

[Guest]

Jane's income is 60% more than Larry's income, and Larry's income is 40% less than Joe's income. What percent of Joe's income is Jane's income?
A) 124%
B)120%
C) 96%
D)80%
E) 64%

OA is C

I am getting two different results if I do it in two different ways. Method 1 leads me to an answer that is not even here. Method 2 gives me the right answer. Can anyone please tell me what I am doing wrong in Method 1

Method 1

Let Larry's income = $100
Then Jane's income = $160 ( 60% more than Larry )
And Joe's income = $140 ( Larry is 40% less than Joe. So Joe is 40% more than Larry. )

(160/140) x 100 = 115% ( apprx)


Method 2
Let Joe's income = $100
Then Larry's income = $60 ( 40% less than Joe )
And Jane'sincome = $96 ( 60% more than Larry)

This yields the right answer of 96%

Thanks

[JonathanSchneider]

The mistake you're making is right here:

"And Joe's income = $140 ( Larry is 40% less than Joe. So Joe is 40% more than Larry. )"

Percentages don't actually work this way. Notice that 40% less than 140 is NOT 100. You want to take away 40%, but what is 40% of 140? It is certainly more than 40. After all, 40 is 40% of 100. But 140 is more than 100, so 40% of 140 must be larger than 40.

Be careful when you pick numbers for problems of this nature. I actually find the problem simpler with algebra:

Jane = 1.6 L
L = .6 Joe
Question: Jane = what % Joe?

Jane = 1.6 L
Jane = 1.6 (.6 Joe)
Jane = .96 Joe