In what ratio must water be mixed with milk so as to make a profit of

Question

In what ratio must water be mixed with milk so as to make a profit of 16*(2/3)% on selling the mixture at a rate same as that of cost price of milk.Given that milk man mixes bottled water instead of tap water and the cost of Bottled water is 20% of the cost of milk

A. 7:41
B. 1:6
C. 6:7
D. 5:23
E. 1:7

A. 7:41
B. 1:6
C. 6:7
D. 5:23
E. 1:7

divyadna · Answer

Total cost price = cost price of milk+ cost price of bottled water

Let CP milk=100$
Therefore, CP bottled water= 20$

Given, profit = 50/300= CP/6

SP-CP=CP/6
SP= 7CP/6

Suppose 10L of milk (mixed with water) is sold. Selling Price= 100*10= 1000
And 'x' L of water are mixed.
1000=7{20x+(10-x)100}/6
6000= 7(1000-80x)
6000= 7000-560x
560x= 1000
x= 1000/560
x=25/14

10-x= 10-(25)14= 115/14
x/(10-x)= 25/115= 5:23
Option D is the answer

Posted from my mobile device

gmatophobia · Answer

This question can be solved using logic. Hence, one can avoid being too "variable and equation frenzy" in solving such question. Before we dive into the actual working, let's take a moment to comprehend the information in the question stem. A milk man buys certain amount of milk, mixes it with water (bottled water in this case - ethical milk man

) and sells the mixture at a rate same as that of cost price of milk, thereby earing \frac{50}{3} % profit Now, the question that arises at this point - How is the milk man even making a profit in entire the transaction as the information states that he sells the mixture at the same rate as that of the cost price of the milk ? If we look carefully, the milk-man is actually saving 80% of the cost per unit of milk that he replaces with the per unit of bottled water , and it's this saving that turns into profit when he sells the milk at the same rate as that of the cost price of the milk. Why 80% ? The cost of bottled water is 20% the cost of the milk Let's assume that the milk-man has one unit of milk with him and the cost of each unit of milk (pure milk) is $1. From this one unit of milk, he takes out x unit (so he takes out milk worth $x) and replaces it with water (that costs him $0.2x), thereby saving 0.8x in the transaction. Profit% = Amount Earned / Cost Price * 100 The cost price of the mixture = Cost of the milk ( i.e. $(1-x) ) + Cost of the bottled water (i.e. $0.2x) \frac{0.8x }{ (1-x + 0.2x)} * 100 = \frac{50}{3} \frac{0.8x }{ (1-0.8x)} * 2 = \frac{1}{3} 4.8x = 1 - 0.8x 5.6x = 1 x = \frac{10}{56} x = \frac{5}{28} Water ⇒ x = \frac{5}{28} Milk ⇒ 1 - Water = 1 - \frac{5}{28} = \frac{23}{28} Milk : Water = \frac{5}{23} Option D

Purnank · Answer

Let n is total quantity of mixture,
And w is amount of water.
Therefore amount of milk = n-w
Price of water to milk given = 1:5
And we are selling mixture on cost price of milk plus we want to make a profit of 50/3 %
So,
Profit=SP-CP=CP/6
Makes SP=7*CP/6
here SP = n*5
And CP =  
n*5 = 7* /6
On solving we get ratio w/n = 5/28

w/n-w = 5/23
Answer is D.

Posted from my mobile device

Kinshook · Answer

In what ratio must water be mixed with milk so as to make a profit of 16*(2/3)% on selling the mixture at a rate same as that of cost price of milk.

Given that milk man mixes bottled water instead of tap water and the cost of Bottled water is 20% of the cost of milk

Let the ratio of water be mixed with milk be k and cost price of milk per liter be x
Milk = 1 liter
Water = k liter
Total = (1+k) liters
Total cost for (1+k) liters of mixture = x + .2xk = x(1+.2k)
Total cost of 1 liters of mixture = x(1+.2k)/(1+k) 
Selling price of 1 liters of mixture after 50/3% profit = x(1+.2k)/(1+k) (1+50/300) = 7x(1+.2k)/6(1+k) = The cost price of 1 liters of milk = x

7(1+.2k) = 6(1+k)
k = 5/23

IMO D

In what ratio must water be mixed with milk so as to make a profit of

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

In what ratio must water be mixed with milk so as to make a profit of

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