A milkman has a solution of milk and water in the ratio

Question

A milkman has a solution of milk and water in the ratio 8:1.He takes one-third of this solution and replaces it with water. If he sells the solutions (both initial and final) at the cost price of pure milk, what is the ratio of profit percentages from initial and final solution? Assume that water does not cost anything.

A. 2:11
B. 4:9
C. 3:7
D. 8:9
E. 13:23

(adapted from gmatfree)

A. 2:11
B. 4:9
C. 3:7
D. 8:9
E. 13:23

(adapted from gmatfree)

Kinshook · Answer

Given: A milkman has a solution of milk and water in the ratio 8:1.He takes one-third of this solution and replaces it with water.

Asked: If he sells the solutions (both initial and final) at the cost price of pure milk, what is the ratio of profit percentages from initial and final solution? Assume that water does not cost anything.

A milkman has a solution of milk and water in the ratio 8:1.
Milk = 8k
Water = k
Solution = 9k
Profit percentage = (9k/8k - 1) = 1/8

He takes one-third of this solution and replaces it with water. 
Milk= 8k - 3k*8/9 = 8k - 8k/3 = 16k/3
Water = k - 3k*1/9 + 3k = 4k - k/3 = 11k/3
Solution = 9k
Profit percentage = 9k/(16k/3) - 1 = 27/16 - 1 = 11/16

Ratio of profit percentage of initial and final solution = (1/8)/(11/16) = 16/88 = 2/11

IMO A

wadhwakaran · Answer

Total Milk=90 ltr
Cost of milk=Rs. 10/ltr
Total Selling Price = 900
Case 1 When m/w=8/1

out of 90 ltr= 80 ltr is milk and 10 ltr is water 
Cost of solution = 80*10=800
Profit = 100
Profit percentage(PP1)= 100/800*100=100/8

Case 2 when 1/3 of solution is taken out from case 1 and is replaced with water

final milk after replacement = initial*concentration remaining=80*2/3=160/3
final water after replacement = 90-160/3=110/3
Cost of solution = 160/3*10=1600/3
profit= 900-1600/3=1100/3
profit percentage (PP2)= 1100/3/1600/3*100=1100/16

PP1/PP2=100/8/1100/16=16/8*11=2/11
 Option A

Archit3110 · Answer

seems to be a CAT question rather a gmat question... nevertheless good for practise.

KarishmaB · Answer

Initial solution milk : water = 8 : 1
So if cost price is 8, selling price is 9 i.e. profit is 1/8 = 2/16

Final solution is a mix of 2 parts milk:water = 8:1 and 1 part only water.
Using concentration of milk, we get
 \frac{2}{1} = \frac{0 - Cavg}{Cavg - 8/9} 
 Cavg = \frac{16}{27}  = Milk concentration in final solution

So if cost is 16, selling price is 27 which means profit is 11/16

Then ratio of profit percentages is 2/16 : 11/16 = 2:11

Answer (A)

bumpbot · Answer

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A milkman has a solution of milk and water in the ratio

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