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

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qlx
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A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   17 Mar 2014, 07:34
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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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   17 Mar 2014, 07:57
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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.

Answer: A.
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   29 Apr 2014, 22:20
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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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   18 Mar 2014, 10:39
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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, \(x =\frac{1}{10}\)

Answer: (A)
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   24 Mar 2014, 07:15
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I think, generally speaking, proportional profit should be calculated on revenue (Rs. 8), rather than cost (Rs. 6,4). Anyone please explains this?
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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?


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

\(% Profit = \frac{(SP-CP)}{CP}* 100 %\)
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   30 Apr 2014, 02:10
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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.

Answer: (A)
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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?
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   30 Apr 2014, 23:38
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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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   01 May 2014, 20:33
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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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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?
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   27 Jul 2014, 22:02
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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.
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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?
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   28 Jul 2014, 20:37
Expert Reply
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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   01 Oct 2015, 04:16
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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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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.
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   14 Apr 2016, 08:03
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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 :lol:
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink] New post   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!
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Re: A dairyman pays Rs. 6.40 per liter of milk. He adds water [#permalink]
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