Man spending Percentages

[eaakbari]

What is the FASTEST method to solve the question given below.


A man spends 70% of his salary on food expenses, 40% of the rest on traveling expenses, 90% of the rest on house rent and was finally left with $3600. How much did he spend on traveling expenses?


A. 24000


B. 18000


C. 25000


D. 22000



E. 20000

[GMATGuruNY]

What is the FASTEST method to solve the question given below.


A man spends 70% of his salary on food expenses, 40% of the rest on traveling expenses, 90% of the rest on house rent and was finally left with $3600. How much did he spend on traveling expenses?


A. 24000


B. 18000


C. 25000


D. 22000



E. 20000

To determine the ratio, let the salary = 1000.

Food = .7(1000) = 700.
Remainder = 1000-700 = 300.
Travel = .4(300) = 120.
Remainder = 300-120 = 180.
Since 90% of the remainder is spent on rent, the amount left after rent = .1(180) = 18.

Travel : amount left = 120:18.

Since the ACTUAL amount left = 3600, and 3600/18 = 200, the multiplier for the ratio is 200:
Travel : amount left = 200(120:18) = 24000:3600.
Thus, travel = 24000.

The correct answer is A.

[Brent@GMATPrepNow]

A man spends 70% of his salary on food expenses, 40% of the rest on traveling expenses, 90% of the rest on house rent and was finally left with $3600. How much did he spend on traveling expenses?

A. 24000
B. 18000
C. 25000
D. 22000
E. 20000

Another approach is to work backwards.

At the end, the man spent 90% of some amount on house rent and was finally left with $3600.
So, if X = the $ he had before paying the rent, we know that:
- 90% of X = rent
- The remaining 10% of X = 3600 (in other words, 0.1X = 3600)
This tells us that X = 36,000
In other words, he had $36,000 BEFORE paying the rent.

Now move back a step.

The man spent 40% of some amount on travel and was left with $36,000.
So, if Y = the $ he had before paying for travel, we know that:
- 40% of Y = travel
- The remaining 60% of Y = 36,000 (in other words, 0.6Y = 36,000)
We can solve this equation to see that Y = 60,000

So Y = 60,000 and 40% of this was spent on travel.
40% of 60,000 = 24,000 so the answer is A

Cheers,
Brent