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

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Manager
Joined: 29 Nov 2018
Posts: 61
Concentration: Marketing, Strategy
If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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29 Dec 2018, 14:15
1
5
00:00

Difficulty:

65% (hard)

Question Stats:

44% (02:31) correct 56% (01:46) wrong based on 57 sessions

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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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Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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29 Dec 2018, 18:42
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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Manager
Joined: 01 May 2017
Posts: 68
Location: India
If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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29 Dec 2018, 18:55
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
VP
Joined: 18 Aug 2017
Posts: 1162
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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30 Dec 2018, 01:25
1
1
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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Director
Joined: 27 May 2012
Posts: 665
Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost  [#permalink]

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15 Jan 2019, 20:15
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?
_________________

- Stne

Re: If a milkman wishes to earn a profit of 16.66% by selling milk at cost &nbs [#permalink] 15 Jan 2019, 20:15
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# If a milkman wishes to earn a profit of 16.66% by selling milk at cost

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