A dishonest milkman mixes water and milk and claims to sell the milk

Question

A dishonest milkman mixes water and milk and claims to sell the milk at cost price, thereby making a profit of 25%. How much water is there in one litre that he delivers to the customers?

A) 200 ml 
B) 250 ml 
C) 166.66 ml 
D) 180 ml
E) 320 ml

Chethan92 · Answer

Let the cost price of milk be 1.
Let the cost price of water be 0 (as it's freely available)
He's selling the mixture at CP with 25% profit.
Using Allegation method.

Please check the attachment

Final ratio is 4(milk):1(water)

Water in 1liter of milk = 1000/5 = 200ml

A is the answer.

GMATGuruNY · Answer

Let the cost per ml = $1, implying that the milkman sells the 1000-ml mixture for $1000.
For every $4 in cost, the milkman must make $1 in profit -- a profit of 25% -- yielding a selling price of $5.
Implication:
Of every $5 in the selling price, $4 = cost, $1 = profit.
Since the cost is equal to 4/5 of the selling price, we get:
Cost = (4/5)(1000) = $800, profit = 1000-800 = $200.
Thus, the 1000-ml mixture is composed of 800 ml of milk (at a cost of $800) and 200 ml of water (at a cost of $0).

A

Gladiator59 · Answer

Let 1000ml milk cost $100. That's some expensive milk

no wonder milkman is cheating The milkman is adding some amount, say x ml in the milk and selling 1000ml of this mixture for 100 (the cost price claimed by milkman) and making 25% profit. For someone to make 25% profit, the selling price should be 1.25 times the cost price. So, for the milkman, the cost of 1000 ml of the mixture is 100/1.25 or $80. So the milkman needs only $80 for a mixture of 1000 ml -> meaning only 800ml is milk and hence the remaining 200ml is water. Hope this is helpful.

Mislead · Answer

A better way to look at the question is, if the merchant is selling something at a profit of 25% what is its cost price.

We can use a relation that if something increases by 1/4 i.e. 25%, we have to reduce that something by 1/5 i.e. 20% to come down to the original price.

1000 needs to be reduced by 20% to know what the actual amount of milk is sold at CP that merchant claims.

1000*1/5 =200ml

Ans: A

adewale223 · Answer

Let x be cost of milk

Profit = CP/4

SP = 5CP/4

x(w + m) = 5(mx)/4

Amount of water in one litre

5 ( 1- w)x/4 = x

5( 1-w ) = 4

1 - w = 4/5

-w = - 1/5

w = 1/5 l

Convert to ml

1/5 x 1000

= 200ml

Answer A

Adewale Fasipe, GMAT quant instructor Lagos Nigeria.

Oppenheimer1945 · Answer

Let there be mix of W lt of water
Price be 1Rs/lt

SP for 1 lt=1Rs
Actual CP for 1 lt=1/(1+W) Rs

1.25(1/(1+W))=1
=>W=1/4 lt=250ml

bumpbot · Answer

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

A dishonest milkman mixes water and milk and claims to sell the milk

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A dishonest milkman mixes water and milk and claims to sell the milk

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards