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# A dishonest milkman professes to sell his milk at cost price

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Senior Manager
Joined: 21 Aug 2016
Posts: 261
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
A dishonest milkman professes to sell his milk at cost price  [#permalink]

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30 Nov 2016, 09:49
4
8
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:31) correct 38% (01:20) wrong based on 140 sessions

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A dishonest milkman professes to sell his milk at cost price but he mixes it with water. Find the percentage of water in the mixture.

1. By adding water, the milkman gains 25%.

2. Milk in the new mixture is 80%.

--------------------------------

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Manager
Joined: 02 Nov 2013
Posts: 81
Location: India
Re: A dishonest milkman professes to sell his milk at cost price  [#permalink]

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30 Nov 2016, 10:51
1
Hi, Very interesting question. Before answering this, I read the question 4-5 times.
I think the answer is D.
Senior Manager
Joined: 21 Aug 2016
Posts: 261
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
A dishonest milkman professes to sell his milk at cost price  [#permalink]

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30 Nov 2016, 14:34
2
1
prashantrchawla wrote:
Hi, Very interesting question. Before answering this, I read the question 4-5 times.
I think the answer is D.

Correct !

Detailed Solution

Let's say milkman has 100 lt of milk. If he added x lt of water, the percentage of water in the mixture =x*100/(100+x)

Statement1: As the milkman gained 25%, he must have added 25lt water in 100 lt of milk. Then, the percentage of water in the mixture = 25*100/(125) =20%

Statement2 : In the new mixture, if the milk is 80% then 80% of total mixture should be 100 lt

(100+x)*80/100=100
8x=200
x=25
Then, the percentage of water in the mixture = 25*100/(125)=20%

So both statements in themselves are sufficient. The correct answer is D

+1 Kudos if you like the post
Intern
Joined: 13 Jun 2013
Posts: 4
Location: India
Concentration: General Management, Marketing
WE: Engineering (Energy and Utilities)
Re: A dishonest milkman professes to sell his milk at cost price  [#permalink]

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28 Dec 2016, 06:54
Hi
Above algebraic solution works. But Can anyone also suggest a solution for this problem using allegation

Thanks !!
Senior Manager
Joined: 21 Aug 2016
Posts: 261
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
A dishonest milkman professes to sell his milk at cost price  [#permalink]

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28 Dec 2016, 07:46
2
Pochimon wrote:
Hi
Above algebraic solution works. But Can anyone also suggest a solution for this problem using allegation

Thanks !!

Detailed Solution using allegation

Statement 1:

Let cost price of 1 kg milk = Rs.1

selling price of 1 kg mixture = Rs.1

cost price of 1 kg mixture = 1*(100/125)=4/5

cost price of 1 kg water = 0

By rule of allegation,
1 0
\ /
\ /
4/5
/ \
/ \
4/5-0 1-4/5
4/5 1/5

(editor did not allow me to enter the space for above diagram )

Thus we get, quantity of milk : quantity of water = 4:1
Hence, the percentage of water in the mixture =(1/5)*100 %= 20%.

Statement 2:

Suppose there are two liquid -- one water (0% milk) and other milk(100% milk)

when two are mixed, the mixture has 80% milk

0 100
\ /
\ /
80
/ \
/ \
(100-80) 80-0
20 80

quantity of water : quantity of milk =20:80=1:4
Hence, percentage of water in the mixture =(1/5)*100 %= 20%.

Hope it helps.
+1 Kudos if you like the post
Non-Human User
Joined: 09 Sep 2013
Posts: 11011
Re: A dishonest milkman professes to sell his milk at cost price  [#permalink]

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16 Mar 2019, 07:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A dishonest milkman professes to sell his milk at cost price   [#permalink] 16 Mar 2019, 07:55
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