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

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If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 29 Dec 2018, 15:15
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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

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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 29 Dec 2018, 19:42
cfc198 wrote:
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

If you liked the question, please do hit the kudos button :)


Say 1 litre costed 100 ..
Now with profit, 1 litre should cost 100+50/3=350/3..
So selling 1 litre at 350/3 is the same as selling 3/350 litre at 1 or same as 100*3/350 at 100..
So milk is 300/350 or 6/7 and water will be 1-6/7=1/7=14.28%

B
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If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 29 Dec 2018, 19:55
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
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 30 Dec 2018, 02:25
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cfc198 wrote:
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

If you liked the question, please do hit the kudos button :)



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
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 15 Jan 2019, 21:15
chetan2u wrote:
cfc198 wrote:
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

If you liked the question, please do hit the kudos button :)


Say 1 litre costed 100 ..
Now with profit, 1 litre should cost 100+50/3=350/3..
So selling 1 litre at 350/3 is the same as selling 3/350 litre at 1 or same as 100*3/350 at 100..
So milk is 300/350 or 6/7 and water will be 1-6/7=1/7=14.28%


B



Hi chetan2u,
Not able to understand this solution , can you make this a little easier to understand?
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 16 Jan 2019, 14:51
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cfc198 wrote:
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

If you liked the question, please do hit the kudos button :)


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

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Brent
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 22 Jan 2019, 16:28
cfc198 wrote:
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



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%
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 08 Mar 2019, 21:54
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%
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 08 Mar 2019, 23:11
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%.
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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New post 09 Mar 2019, 03:16
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
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Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost   [#permalink] 09 Mar 2019, 03:16
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