Percentage Help!!

[anuu]

Hi All,

Can anyone pls suggest an easier appraoch for the following problem?

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?

I did start of with x as the salary and found the remaining amount at each stage and then applied successive percentage for that stage..this method took me nearly 8 min+

Is there an easier appraoch?

The answer choices are : 24000,18000, 25000,22000, 20000

Regards,
Anu

[pankajks2010]

Let the salary be x. The complete salary is 100%.

Food expense = 70% of x, Therefore the remaining amount is 30% of x (this can be done mentally to save time)

Out of this 30% of x, 40% is spent on travelling, which is (40/100) (30/100) x = 12% of x (this again can be solved mentally)

Thus, the remaining amount is (100-70-12)% or 18% of x. Of this 18%, 90% is spent on house rent. That means the final amount which gets saved is only 10% of (18% of x) which is 1.8% of x.

Now, I'll do some calculations to find out x: x=3600*100/1.8=200,000

Travelling expense is 12% of x: (12/100)*200000=24,000

So, the time saving approach is to calculate the remaining amount by substracting the used percentage directly from 100, this helps to avoid lengthy calculations.
Ex: 1) The amount remaining after food expense was directly calculated as (100-70)% of x
2) The amount left after house rent was calculated as (90-10)% of (18% of x)

Hope it helps!!

[smackmartine]

Back solving is a great method for solving these types of problems

(money left after Paying Travel expense = 90% of "money left after Paying Travel expense" on Rent + $3600 )

Left amount $ 3600 = 10% of money left after Paying Travel expenses

So, money left after Paying Travel expenses = $36000 = 60% of money left after Paying Food expenses

money left after Paying Food expenses = 36000 /0.6 = $ 60,000

Now given that : Travel Expenses = 40% of money left after Paying Food expenses = 0.4 * 60,000 = $ 24000

So A

Hope this helps!

[GmatKiss]

Is this a valid GMAT problem?
Source please!

[smackmartine]

Is this a valid GMAT problem?
Source please!

I would say this is a valid problem, because you can clearly see that there are various methods by which you can solve this problem. Someone took 8min +, while using back solving method,you can solve the problem in 2 min. Back solving is, for sure, tested on GMAT.
I do not know the source though. The original poster should post the source.

[thestartupguy]

I took the salary to be 100 units and solved it. It took me less than a minute to solve.