BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Percentage Help!!

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Wed Feb 23, 2011 9:41 am
Thanked: 1 times

Percentage Help!!

by anuu » Sat May 14, 2011 8:52 am
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
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 118
Joined: Wed Mar 16, 2011 12:51 am
Location: New Delhi, India
Thanked: 12 times
Followed by:1 members

by pankajks2010 » Sat May 14, 2011 9:41 am
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!!
Top
User avatar
Legendary Member
Posts: 516
Joined: Fri Jul 31, 2009 3:22 pm
Thanked: 112 times
Followed by:13 members

by smackmartine » Sat May 14, 2011 10:40 am
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!
Top
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 am
Location: Chennai, India
Thanked: 206 times
Followed by:43 members
GMAT Score:640

by GmatKiss » Sat Sep 03, 2011 10:50 am
Is this a valid GMAT problem?
Source please!
Top
User avatar
Legendary Member
Posts: 516
Joined: Fri Jul 31, 2009 3:22 pm
Thanked: 112 times
Followed by:13 members

by smackmartine » Sat Sep 03, 2011 11:09 am
GmatKiss wrote: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.
Smack is Back ...
It takes time and effort to explain, so if my comment helped you please press Thanks button :)
Top
Master | Next Rank: 500 Posts
Posts: 150
Joined: Thu May 05, 2011 10:04 am
Thanked: 5 times
Followed by:4 members

by thestartupguy » Sat Sep 03, 2011 12:36 pm
I took the salary to be 100 units and solved it. It took me less than a minute to solve.
Top
Post new topic Post Reply
• Page 1 of 1