approved water costs him $4

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Nov 01, 2013 5:11 am

A milkman professes to mix 1 part of approved water in every 3 parts of pure milk to sell. If pure milk costs him $100 per gallon, and the approved water costs him $4 per quart, then at how many dollars (to the nearest integer) per pint must he sell his milk in order to make an overall profit of 25 percent?

1 quart = 2 pints and 1 gallon = 4 quarts
A. $99
B. $25
C. $18
D. $12
E. $8

Made Up

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Source: Beat The GMAT — Problem Solving | Fri Nov 01, 2013 5:11 am

mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Fri Nov 01, 2013 6:29 am

sanju09 wrote:A milkman professes to mix 1 part of approved water in every 3 parts of pure milk to sell. If pure milk costs him $100 per gallon, and the approved water costs him $4 per quart, then at how many dollars (to the nearest integer) per pint must he sell his milk in order to make an overall profit of 25 percent?

1 quart = 2 pints and 1 gallon = 4 quarts
A. $99
B. $25
C. $18
D. $12
E. $8

Is the answer D?

Q: SP = ?

He makes 25% profit thus,
[ (SP - CP)/CP ] * 100 = CP
SP = 1.25 CP

Now the tricky part

Before selling he mixes water in milk in the following ratio
Milk:Water = 3:1

To find Total CP of Milk and Water:

Milk --> 1 Gallon = $100 --> 4 Quarts = $100 --> 8 Pints = $100
Cost per pint = $12.5

Water --> 1 Quart = $4 --> 2 Pints = $4
Cost per pint = $2

Lets suppose he purchases 4 pints of the mix and sells 4 pints of the mix:
Total cost = Cost of 3pints of Milk + Cost of 1Pint of Water ~ $40
CP per pint ~ $10

SP = 1.25 * 10 = 12.5
Closest answer D

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Fri Nov 01, 2013 8:50 am

1W + 3M

Milk Costs = 100$ per gallon => 25$ per Quart ==> 12.5 per PINT
Water = 4$ per quart => 2$ per PINT

Profit = 25%

SP = CP + Profit
= 1.25(CP) = 1.25 ( 1/4*2 + 3/4*12.5) = 1.25 (.5 + ~9) = ~12

Answer [spoiler]{D}[/spoiler]

R A H U L

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Nov 02, 2013 12:14 am

Well done mates! My answer is also D.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Nov 02, 2013 2:56 am

sanju09 wrote:A milkman professes to mix 1 part of approved water for
every 3 parts of pure milk to sell. If pure milk costs him $100 per gallon, and the approved water costs him $4 per quart, then at how many dollars (to the nearest integer) per pint must he sell his milk in order to make an overall profit of 25 percent?

1 quart = 2 pints and 1 gallon = 4 quarts
A. $99
B. $25
C. $18
D. $12
E. $8

Cost of 1 QUART of water = $4.
1 gallon = 4 quarts.
Thus, the cost of 1 GALLON of water = 4*4 = $16.

The mixture = 1 part water + 3 parts milk.
Water = $16 per gallon and milk = $100 per gallon.
Thus, the cost of 1 gallon water + 3 gallons milk (for a total of 4 GALLONS of mixture) = 1*16 + 3*100 = 316 â‰ˆ 320.
Thus, the cost of 1 GALLON of mixture = 320/4 = $80.
1 gallon = 8 pints.
Thus, the cost of 1 PINT of mixture = 80/8 = $10.

To make a profit of 25%, the selling price of 1 pint of mixture = 10 + .25(10) = $12.5.

The correct answer is D.

Pretty expensive milk!
Must be organic.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Nov 14, 2013 1:14 am

GMATGuruNY wrote:.

Pretty expensive milk!
Must be organic.

Why should we worry that if the cat is ready to afford it.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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