GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Aug 2018, 15:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A dairyman pays Rs. 6.40 per liter of milk. He adds water

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Mar 2014
Posts: 68
A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

17 Mar 2014, 07:34
5
18
00:00

Difficulty:

75% (hard)

Question Stats:

62% (03:03) correct 38% (02:28) wrong based on 243 sessions

### HideShow timer Statistics

A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25
Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

17 Mar 2014, 07:57
6
3
qlx wrote:
A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25

Milk = m liters;
Water = w liters;

Cost of m+w liters = 6.4m;
Selling price of m+w liters = 8(m+w).

Given that 6.4m*1.375 = 8(m+w) --> w/m=1/10.

_________________
Manager
Joined: 04 Oct 2013
Posts: 155
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

18 Mar 2014, 10:39
3
1
2
A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25

Assuming proportion of water to milk as x:1, the equation can be written as

[Selling price of (1 liter Milk + x liter Water) - Cost of 1 liter Milk = Profit earned on 1 liter milk]

$$8 (1 +x) - 6.4 = 6.4 (\frac{3}{8})$$ [Since, 37.5% = 3/8]
Or, $$8x - 1.6 = 2.4$$
Or, $$x =\frac{1}{10}$$

##### General Discussion
Intern
Joined: 23 Nov 2011
Posts: 5
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

24 Mar 2014, 07:15
1
I think, generally speaking, proportional profit should be calculated on revenue (Rs. 8), rather than cost (Rs. 6,4). Anyone please explains this?
Manager
Joined: 04 Oct 2013
Posts: 155
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

27 Apr 2014, 10:31
dungnguyenstu wrote:
I think, generally speaking, proportional profit should be calculated on revenue (Rs. 8), rather than cost (Rs. 6,4). Anyone please explains this?

$$Selling Price (SP) = Cost Price (CP) + Profit$$

$$% Profit = \frac{(SP-CP)}{CP}* 100 %$$
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

29 Apr 2014, 22:20
5
1
2
qlx wrote:
A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25

You can reason it out like this:

Selling price is Rs 8 per liter with a profit of 37.5% (which is 3/8) of Cost Price.

Cost Price*(1 + 3/8) = 8
Cost Price = 64/11
So for every liter he sells, he uses only Rs. 64/11 worth of milk.

In Rs 6.4, you get 1 lt of milk
In Rs 64/11 you get 64/(11*6.4) = 10/11 lts of milk

Since he uses only 10/11 lts of milk, he must be putting 1/11 lts of water in it.
So water:milk = 1:10
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Joined: 04 Oct 2013
Posts: 155
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

30 Apr 2014, 02:10
1
A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25

Dairyman would earn 25% profit, if only milk were sold at Rs 8 per liter.
Since the profit earned is 37.5% by selling milk and water, the additional 12.5% profit is due to selling only water.

12.5% of Rs 6.40 is 80p, which can buy 1/10th of a liter of milk from Diaryman.
Therefore, the proportion of water to milk received by the customers is 1:10.

Senior Manager
Joined: 08 Apr 2012
Posts: 395
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

30 Apr 2014, 23:29
VeritasPrepKarishma wrote:

In Rs 6.4, you get 1 lt of milk
In Rs 64/11 you get 64/(11*6.4) = 10/11 lts of milk

Hi...

I am not completely sure why you multiplied the bottom part of the fraction by 6.4.
I can't find the reasoning... can you explain?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

30 Apr 2014, 23:38
1
ronr34 wrote:
VeritasPrepKarishma wrote:

In Rs 6.4, you get 1 lt of milk
In Rs 64/11 you get 64/(11*6.4) = 10/11 lts of milk

Hi...

I am not completely sure why you multiplied the bottom part of the fraction by 6.4.
I can't find the reasoning... can you explain?

I am using the unitary method which goes like this:

If 10 pens cost $30, what is the cost of 18 pens? Cost of 10 pens =$30

Cost of 1 pen = $$\frac{30}{10}$$

Cost of 18 pens = $$\frac{30}{10} * 18$$

I am using the same method here. If you go step by step, it looks like this:

In Rs 6.4, you get 1 lt of milk

In Re 1, you get $$\frac{1}{6.4}$$ lts of milk

In Rs $$\frac{64}{11}$$ you get $$\frac{1}{6.4} * \frac{64}{11} = \frac{10}{11}$$ lts of milk
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Retired Moderator
Joined: 20 Dec 2013
Posts: 180
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

01 May 2014, 19:09
tough one...

I just calculated the cost at which he would make a 37.5% profit, so:

(8/x)-1=37.5/100
x=64/11

his actual cost was 6.4/L = 64/10L

so comparing the two values it becomes apparent that one liter of water is added to 10 of milk
_________________
Manager
Joined: 20 Dec 2013
Posts: 123
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

01 May 2014, 20:33
1
qlx wrote:
A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25

% profit from milk: 1.6/6.4 x 100 = 25 %

For two profits the resultant profit will be: A + B + AB/100

25 + B + 0.25B = 37.5

1.25B = 12.5
B = 10 %

Hence 10 : 1
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Senior Manager
Joined: 08 Apr 2012
Posts: 395
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

27 Jul 2014, 08:32
VeritasPrepKarishma wrote:
ronr34 wrote:
VeritasPrepKarishma wrote:

In Rs 6.4, you get 1 lt of milk
In Rs 64/11 you get 64/(11*6.4) = 10/11 lts of milk

Hi...

I am not completely sure why you multiplied the bottom part of the fraction by 6.4.
I can't find the reasoning... can you explain?

I am using the unitary method which goes like this:

If 10 pens cost $30, what is the cost of 18 pens? Cost of 10 pens =$30

Cost of 1 pen = $$\frac{30}{10}$$

Cost of 18 pens = $$\frac{30}{10} * 18$$

I am using the same method here. If you go step by step, it looks like this:

In Rs 6.4, you get 1 lt of milk

In Re 1, you get $$\frac{1}{6.4}$$ lts of milk

In Rs $$\frac{64}{11}$$ you get $$\frac{1}{6.4} * \frac{64}{11} = \frac{10}{11}$$ lts of milk

Ok that seems fair....
The question that I don't understand now, is why did you check the 64/11 necessarily?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

27 Jul 2014, 22:02
ronr34 wrote:
Ok that seems fair....
The question that I don't understand now, is why did you check the 64/11 necessarily?

Because of the first step. Note that his cost price is not Rs 6.4 per liter. The milk in 1 liter is free. His cost price is only for the amount of milk he puts in the 1 lt.

Selling price is Rs 8 per liter with a profit of 37.5% (which is 3/8) of Cost Price.

Cost Price*(1 + 3/8) = 8
Cost Price = 64/11
So for every liter he sells, he uses only Rs. 64/11 = Rs 5.8 worth of milk. In Rs 5.8, he gets less than 1 lt of milk. The rest is water in every liter he sells.

That is how you get 64/11 as the cost price.
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Senior Manager
Joined: 08 Apr 2012
Posts: 395
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

28 Jul 2014, 12:20
VeritasPrepKarishma wrote:
ronr34 wrote:
Ok that seems fair....
The question that I don't understand now, is why did you check the 64/11 necessarily?

Because of the first step. Note that his cost price is not Rs 6.4 per liter. The milk in 1 liter is free. His cost price is only for the amount of milk he puts in the 1 lt.

Selling price is Rs 8 per liter with a profit of 37.5% (which is 3/8) of Cost Price.

Cost Price*(1 + 3/8) = 8
Cost Price = 64/11
So for every liter he sells, he uses only Rs. 64/11 = Rs 5.8 worth of milk. In Rs 5.8, he gets less than 1 lt of milk. The rest is water in every liter he sells.
That is how you get 64/11 as the cost price.

Hi Karishma,
Perhaps i've looked at this question so long that I don't see things anymore.
But still not seeing where you get "11" from...
Is there another way you can explain this to me in?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

28 Jul 2014, 20:37
ronr34 wrote:
VeritasPrepKarishma wrote:
ronr34 wrote:
Ok that seems fair....
The question that I don't understand now, is why did you check the 64/11 necessarily?

Because of the first step. Note that his cost price is not Rs 6.4 per liter. The milk in 1 liter is free. His cost price is only for the amount of milk he puts in the 1 lt.

Selling price is Rs 8 per liter with a profit of 37.5% (which is 3/8) of Cost Price.

Cost Price*(1 + 3/8) = 8
Cost Price = 64/11
So for every liter he sells, he uses only Rs. 64/11 = Rs 5.8 worth of milk. In Rs 5.8, he gets less than 1 lt of milk. The rest is water in every liter he sells.
That is how you get 64/11 as the cost price.

Hi Karishma,
Perhaps i've looked at this question so long that I don't see things anymore.
But still not seeing where you get "11" from...
Is there another way you can explain this to me in?

Do you see how we get: Cost Price*(1 + 3/8) = 8?
We used the formula: Cost Price*(1 + Profit%) = Sale Price
Since Profit is 37.5%, it is equivalent to 3/8.

Cost Price * ( 1 + 3/8) = 8 (which is the sale price)
Cost Price * (11/8) = 8
Cost Price = 8*8/11 (Multiply both sides by 8 and then divide both sides by 11)
Cost Price = 64/11
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Senior Manager
Joined: 20 Aug 2015
Posts: 392
Location: India
GMAT 1: 760 Q50 V44
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

01 Oct 2015, 04:16
Given: Selling price of the mixture = 8/lt
Cost price of Milk = 6.4/Lt
Profit Percentage = 37.5%

Required: Proportion of water to milk
We know that SP = CP + Profit
or Profit = SP - CP

Let us assume 'm' liters of milk and 'w' liters of water
$$8(m+w) - 6.4m = (37.5/100)*6.4m$$
$$8w + 1.6m = 2.4m$$
$$8w = 0.8m$$

or $$w/m = 1/10$$

Option A
Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water  [#permalink]

### Show Tags

26 Feb 2016, 20:02
requires some outside the box thinking rather than applying formulas...
suppose 1 water, 20 milk. milk costs = 128$. sells 21 liters for 168. difference 40. 40/128 = 10/32 = 5/16 2.5/8, but we need 3/8. so 20 out, and so is E. (~30%) let's take A: 10*6.4 = 64$
+1 liter - total 11 liters.
sold for 88$88-64=24. now 24/64 = 12/32 = 6/16 = 3/8. matches. Current Student Joined: 12 Aug 2015 Posts: 2650 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] ### Show Tags 14 Apr 2016, 07:25 Okay Maybe i am Going a Bit OverBoard Here But What if Water Wasn't actually Free ? It has costs associated with it too right? What Do you think Abhishek009 _________________ MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs! STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+) AVERAGE GRE Scores At The Top Business Schools! Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3816 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] ### Show Tags 14 Apr 2016, 08:03 1 stonecold wrote: Okay Maybe i am Going a Bit OverBoard Here But What if Water Wasn't actually Free ? It has costs associated with it too right? What Do you think Abhishek009 For allegation problems we must always consider cost of water as 0. The objective of the dishonest trader is to always maximize his profits by adding some impurities to the product they are selling. Further in doing so their objective is to add some impurities whose cost is as low as possible ( To maximize profits).. Water being an universal solvent and is the most easily available commodity we can assume the cost price of water as nil. Such problems are very common to alligation problems in various shapes like ( wine and water , milk and water etc....) and it is considered safe to take price of water as zero. Hope that helps !! :-D _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern Joined: 29 Mar 2017 Posts: 25 GMAT 1: 750 Q50 V40 Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] ### Show Tags 23 May 2017, 03:25 VeritasPrepKarishma wrote: qlx wrote: A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is (a) 1:10 (b) 1:12 (c) 1:15 (d) 1:20 (e) 1:25 You can reason it out like this: Selling price is Rs 8 per liter with a profit of 37.5% (which is 3/8) of Cost Price. Cost Price*(1 + 3/8) = 8 Cost Price = 64/11 So for every liter he sells, he uses only Rs. 64/11 worth of milk. In Rs 6.4, you get 1 lt of milk In Rs 64/11 you get 64/(11*6.4) = 10/11 lts of milk Since he uses only 10/11 lts of milk, he must be putting 1/11 lts of water in it. So water:milk = 1:10 Karishma - Can you please confirm whether the GMAT officially defines profit margin this way? In the U.S. financial services industry, profit margin is uniformly calculated as a percent of revenue (i.e. (Revenue - Cost) / Revenue). Hence, 37.5% profit margin would be 37.5% of$8 sales price, as opposed to \$8 = Cost Price * (1+37.5%). Just want to make sure this is an official GMAT definition and not a cultural difference as I noticed the problem was written with Rs. being the currency. Thanks!
Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water &nbs [#permalink] 23 May 2017, 03:25

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.