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?

(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 6:11

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.

Answer choice C: W:M = 1:8.
Cost of 1 liter of water and 8 liters of milk = (1*0) + (8*33) = 264.
Selling price of 9 liters of mixture = 9*36 = 324.
Profit/Cost = (324-264)/264 = 60/264 = 15/66 = 5/22 = more than 20%.
Incorrect: the required profit is 20%.
To REDUCE the profit, MORE MILK must be used.
Eliminate C, 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.

Milkman sells at Rs. 36 a litre and makes a profit of 20 percent . His cost price is 36 x (100/120) = Rs 30

From here onwards we can use the concept of. Mixture and allegation to solve the question extremely fast.

Water. ..................................... Milk

0 Rs per litre .......................... 33 (as milk costs. Rs 33 per litre)

.......................................... 30 ( this Is the resultant when he mixes water at Rs 0 per litre and milk at 33 per litre)

.........3 ( 33-30)............................... 30 ( 30 - 0 )

Now the ratio between Water and milk is 3 : 30 . This when simplified gives a ratio of 1: 10. Hence the answer is. B.

Note Whenever two quantities are mixed to get a third quantity we can use method of mixture and allegation.