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

Redeem

Mixture Question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Mon Mar 02, 2009 6:27 pm

Mixture Question

by nadib002 » Sat May 07, 2011 11:57 am
5 litres of water is added to a certain quantity of pure milk costing $3 per litre. If, by selling the mixture at the same price as before a profit of 20% is made, what is the amount of pure milk in the mixture?

My approach:

Quantity of milk = x lts

Cost of milk per lt = $3


Water added = 5 lt

Total quantity of mix = x+5 lts

Selling Price of milk = 3x


Mixture (x+5) lts is also sold at $3 per lt. Therefore SP of mixture = 3(x+5)

I am stuck after this. How do i set up the 20% profit?

Help needed.

Thank you
Top
Source: — Problem Solving |
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 07, 2011 4:27 pm
I think if you had posted the options, you would have gotten some reply. Anyways

Let the quantity of pure milk is x

so , total cost of x liter @ $3 per liter will be 3x
After adding 5 liters of water and selling @ same rate, New Total cost is 3(x+5)

As per question , profit is 20% => [3(x+5)-3x]/3x =1/5

15/3x = 1/5 => x = 25 . So, initial quantity of milk was 25 liters.

Now if you want to cross verify the answer :

Initial quantity of milk = 25 liters , Total cost = 3*25 = $ 75
After adding 5 liters of water and selling the solution @ same rate, the total cost will be 3*(25+5)= $90

Now, profit = [(90-75)/75 ]*100 = [15/75]*100 = [1/5]*100 = 20 (which is given)

nadib002 wrote:5 litres of water is added to a certain quantity of pure milk costing $3 per litre. If, by selling the mixture at the same price as before a profit of 20% is made, what is the amount of pure milk in the mixture?

My approach:

Quantity of milk = x lts

Cost of milk per lt = $3


Water added = 5 lt

Total quantity of mix = x+5 lts

Selling Price of milk = 3x


Mixture (x+5) lts is also sold at $3 per lt. Therefore SP of mixture = 3(x+5)

I am stuck after this. How do i set up the 20% profit?

Help needed.

Thank you
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat May 07, 2011 5:24 pm
nadib002 wrote:5 litres of water is added to a certain quantity of pure milk costing $3 per litre. If, by selling the mixture at the same price as before a profit of 20% is made, what is the amount of pure milk in the mixture?

My approach:

Quantity of milk = x lts

Cost of milk per lt = $3


Water added = 5 lt

Total quantity of mix = x+5 lts

Selling Price of milk = 3x


Mixture (x+5) lts is also sold at $3 per lt. Therefore SP of mixture = 3(x+5)

I am stuck after this. How do i set up the 20% profit?

Help needed.

Thank you
The cost of the milk is irrelevant.
Let m = volume of the pure milk.
To make a 20% profit, the added water must increase the volume of the pure milk by 20%.
Thus, the 5 liters of added water must be 20% of the volume of the milk:
5 = .2m
m = 5/.2 = 25.

For many test-takers, the easiest approach would be the plug in the answers, which would represent the amount of milk:

Answer choice: 25 liters of milk
Cost at $3 per liter = 3*25 = $75.
Volume of mixture = milk + water = 25+5 = 30 liters.
Selling price = 3*30 = $90.
Profit = 90-75 = 15, which is 20% of the cost of the milk.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1