Pls help: More Gperp problems

[rezwanamannan]

In May, Mrs. Lee’s earnings were 60% of the Lee’s family Income. In June, Mrs. Lee earned 20% more than in May. If the rest of the family’s income was the same both months, then, in June, Mrs. Lee’s earnings were approximately what % of the Lee family’s total income?
a) 64%
b) 68%
c) 72%
d) 76%
e) 80%

OA- A, but my answer come to 72%. CAn someone help?

[RonPurewal]

first, please follow the directions regarding how to name posts: first several words of the question title.
this rule is especially important for facilitating future searches; please follow it. thank you.
i have take the liberty of changing the title of this post.

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you are making the mistake of assuming that percentages act like "normal" numbers; you just increased 60 itself by 20%, giving 72.
unfortunately, percentages are more complicated than that.

let me give you an example to show you the fallacy in your reasoning: let's say that mrs. lee's income doubles.
under your reasoning, then, you'd say that mrs. lee is now earning 120% of the family's income, a statement that is patently ridiculous.

the problem is that, when you increase one component of something (mrs. lee's income, in this case), the total also increases.
so, while mrs. lee's new income would indeed be 72% (or 120%, in my example) of the OLD total, it's not 72% (or 120%) of the NEW total. it's less, because the new total is larger than the old total.

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the easiest way to solve this problem is to PLUG IN NUMBERS.
let's let the original family income be $100. this means mrs. lee originally made $60.
after a 20% increase, she now makes $72 -- but the family income is now $112. therefore, the desired percentage is 72/112, which works out to approximately 64.3%.