Percent

vinay1983 wrote:A man spends 20% of his income on rent, 15% of the balance on groceries, and 30% of the balance after spending on groceries on conveyance and is left with $ 1190. What is his income?

OA:[spoiler]$2500[/spoiler]

Let I = man's income.

Man spends 20% of his income on rent
If 20% of income is spent on rent, then 80% of income remains.
So, amount remaining (balance) = 0.8I

Man spends 15% of the balance on groceries
If 15% of balance is spent on groceries, then 85% of balance remains.
So, amount now remaining = (0.85)(0.8I)

Man spends 30% of the remaining balance on conveyance
If 30% of balance is spent on conveyance, then 70% of balance remains.
So, amount remaining = (0.7)(0.85)(0.8I)

Man is left with $1190
So, (0.7)(0.85)(0.8I) = 1190

Aside: At this point, this question seems unGMAT-like since these calculations are somewhat tedious, and the GMAT test-makers aren't really interested in our ability to perform boring calculations.

One option is to convert to fractions to get:
(7/10)(17/20)(4/5)I = 1190
Then multiply both sides by reciprocals: I = (1190)(10/7)(20/17)(5/4)
From here, the calculations are a pain, but we end up getting I = 2500

Cheers,
Brent

Hey Vinay1983,

What's the source of the practice questions you've been posting?
Some of them require too many tedious calculations.
Also, given the fact that you don't provide the answer choices, I suspect that they might be questions from a highschool math text.

Cheers,
Brent