If a milkman wishes to earn a profit of 16.66% by selling milk at cost

Question

If a milkman wishes to earn a profit of 16.66% by selling milk at cost price and mixing water to the milk. What percent of the mixture has to be water?

A 12.5
B 14.28
C 20
D 25
E 35

BrentGMATPrepNow · Accepted Answer

I'm assuming that the 6's go on forever (as in 16.66666....%)
16.66666....% = 1/6

So, we're looking for a profit that is 1/6 the wholesale cost. 
A NICE value to start with is a $6 wholesale cost.
So, let's say, the milkman buys 6 liters of milk for a total of $6 ($1/liter)

If the milkman adds 1 liter of WATER to the 6 liters of milk, he then has 7 liters of diluted milk. 
If he sold all 7 liters of diluted milk at the same price of $1/liter, he'd make $7 for a 16.6666...% profit. 
Similarly, if he sells 6 liters of diluted milk at the same price of $1/liter (total price = $6), then his profit is still 16.6666...%

What percent of the mixture has to be water?  
The 7 liters of diluted milk is comprised of 1 liter of water. 
1/7 ≈ 14%

Answer: B

Cheers,
Brent

Archit3110 · Answer

let 1 liter of milk cost $100; selling price 
so profit of 16.66% means that milk has to be sold at 100*1.166= $116.66
since the plan is to sell milk at cost price 
difference in price = 116.66-100 = $16.66
so % of water to be added would be 16.66/116.66 = 14.28% IMO B

chetan2u · Answer

Say 1 litre costed 100 ..
Now with profit of 16.66 or 50/3 %, 1 litre should cost 100+50/3=350/3..
So for 350/3, we get 1 litre. 
And for 1, we get 3/350 litre 
Finally for 100, we get 100*3/350=300/350
So milk is 300/350 or 6/7 and water will be 1-6/7=1/7=14.28%

B

Dare Devil · Answer

Let the Cost Price of Milk(1 liter) = 1 
C.P of water = 0
Then, Selling price of the Milk = 1

Profit = 16.6%
C.P of 1 liter Mixture =  100/116.66

C.P= 0.8571
Mean Price = C.P of Mixture
Water/Milk =  (C.P of Milk - Mean Price)/(Mean Price - C.O of Water) 
 =  (1 - 0.8571)/(0.8570 - 0) 
 =  0.1429/0.857 
So, out of one liter 0.1429*100 = 14.29 % is water

stne · Answer

Hi  chetan2u , 
Not able to understand this solution , can you make this a little easier to understand?

NinetyFour · Answer

My reasoning if it helps anyone:

Let's assume we were originally selling 100ml of milk for $100.

To get a profit of 16.667% or  \frac{1}{6} . we need:

x * \frac{7}{6} = 100 
 x = \frac{600}{7}

Since our milk is priced at $1/ml, it's fair to say we have  \frac{600}{7}  ml of milk in our mixture and the rest is water. Water is free so by replacing part of our milk with water we can make an additional 16.667% profit.

Total amount in our mixture is 100ml or  \frac{700}{7} .

\frac{700}{7} - \frac{600}{7} = \frac{100}{7}ml of water .

% of water in our solution = total ml of water : total ml of solution

\frac{100}{7}/\frac{700}{7}

or 1/7 = 14.28%

LoneSurvivor · Answer

Knowing fractions comes handy. 16.66%=1/6
So The milkman actually sell 6 rupees milk at (6*1/6 +1)=7 rupees.
So amount of water added was 1 litre.
So fraction of water added 1/7=14.28%

ankitsood5 · Answer

Let the quantity be 100 and the CP is 100. => 1 unit costs 1
Now SP is also 100 after a profit of 16.66%. i.e. SP of 100 has arrived after a profit of 16.66%.
Therefore, CP = 100/1.166 = 85.76.
Now, Quantity for an amount of 85.76 = 85.76 i.e. pure milk = 85.76 => Water in 100 => 100-85.76 = 14.23.
14.23/100 = 14.23%.

m1033512 · Answer

Here percent profit = 16.66% = 1/6

So , let the original milk be x then 
water has to be added = the profit which he is expected to earn = 1/6 of original mixture ( here it is milk , x litre)

So total mixture = x+x/6 = 7x/6 ( after adding the water to milk ).

Now percent of water = (x/6)/(7x/6) = 1/7 = 14.28%

IMO B

GMATinsight · Answer

Suppose that the milkman has 100 litres of milk costing $1 per liter

i.e. his revenue = $116.66

Since seller professes to sell at cost price which is $1 per liter therefore quantity that he sells = 116.66 litres

So he is making 100 litres of milk into a 116.66 litres liters of Milk water solution by adding pure water to it

i.e. QUantity of Water added = 116.66 - 100 = 16.66 litres

Water as % of Mixtures = (16.66/116.66)*100 = 14.28%

Hint: 16.66 = 100/6

Answer Option B

chandy123 · Answer

Solution:

To determine the percentage of water that needs to be mixed with milk to achieve a 16.66\% profit by selling the mixture at the cost price of pure milk, follow these steps:

Given:
- Profit Desired: 16.66\%
- Selling Price of Mixture: Same as the Cost Price of pure milk.

Assumptions:
- Let’s assume the Cost Price (CP) of pure milk is \$1 per liter.
- Water is free (i.e., no cost).

Let:
\ 
\ 
\

Profit Calculation:

Profit Percentage Formula:
\

Since the selling price is the same as the cost price of pure milk, the profit comes from using less milk and adding water.

Profit from Mixing:
\

Solving for $ x $:
\ 
\

This implies that for every 6 parts of milk, there are 1 part of water:
\

Total Parts in Mixture: $ 6 + 1 = 7 $

Percentage of Water in the Mixture:
\

Answer:
B) 14.28\%

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If a milkman wishes to earn a profit of 16.66% by selling milk at cost

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