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

Question

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

Bunuel · Accepted Answer

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.

KarishmaB · Answer

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

arunspanda · Answer

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

8 (1 +x) - 6.4 = 6.4 (\frac{3}{8})   
Or,  8x - 1.6 = 2.4 
Or,  x =\frac{1}{10}

Answer:  (A)

dungnguyenstu · Answer

I think, generally speaking, proportional profit should be calculated on revenue (Rs. 8), rather than cost (Rs. 6,4). Anyone please explains this?

arunspanda · Answer

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

% Profit = \frac{(SP-CP)}{CP}* 100 %

arunspanda · Answer

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)

ronr34 · Answer

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?

KarishmaB · Answer

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

m3equals333 · Answer

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

PerfectScores · Answer

% 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

ronr34 · Answer

Ok that seems fair....
The question that I don't understand now, is why did you check the 64/11 necessarily?

KarishmaB · Answer

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.

ronr34 · Answer

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?

KarishmaB · Answer

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

TeamGMATIFY · Answer

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

mvictor · Answer

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.

stonecold · Answer

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

Abhishek009 · Answer

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:

jy295 · Answer

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!

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

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

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