Problem Solving

A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water
(costing nothing) with milk costing Rs.33 per litre so as to make a profit of 20% on cost when
he sells the resulting milk and water mixture for Rs.36 In what ratio should he mix the water
and milk?

to make a 20% profit the selling price must be Rs. 30:

30 (1.2) = 36

To get a weighted cost of 30 from 33 and 0, the ratio must be 10:1 for milk to water:

0(x) + 33(1 - x) = 30 --> x is the percent of the combined solution that is water solution

33 - 33x = 30 --> x = 1/11

This is a part to whole ratio, so the answer is again 10:1 for milk to water.

I've added the phrase in red to clarify the intent of the problem:

spd143 wrote:A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing $33 per liter so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for $36 per liter. In what ratio should he mix the water and milk?
,
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 6:11

We can PLUG IN THE ANSWERS, which represent the ratio of water to milk.
When the correct answer choice is plugged in, the milkman will earn a profit of 20%.

Answer choice D: W:M = 1:4.
Cost of 1 liter of water and 4 liters of milk = (1*0) + (4*33) = 132.
Selling price of 5 liters of mixture = 5*36 = 180.
Profit/Cost = (180-132)/132 = 48/132 = 4/11 = almost 40%.
To REDUCE the profit, MORE MILK must be used.
Eliminate D and E.

Answer choice B: M:W = 1:10
Cost of 1 liter of water and 10 liters of milk = (1*0) + (10*33) = 330.
Selling price of 11 liters of mixture = 11*36 = 396.
Profit/Cost = (396-330)/330 = 66/330 = 11/55 = 1/5 = 20%.
Success!

The correct answer is B.