Let I = man's income.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]
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
