theCodeToGMAT wrote:
The milkman bought milk at Rs 4.5/liter and sold for Rs 5.4/liter. If the profit made by him is 33 1/3 %, then what is the ratio of Milk & Water. (Assume cost of Water = 0)
If no water is added, (selling price)/(cost) = (5.4)/(4.5) = 6/5.
Since 6/5 is equal to 1/5 above cost, the profit if no water is added is equal to 1/5.
We need determine by what factor the volume must increase so that the profit is equal to 1/3 -- in other words, so that price/cost = 4/3:
(6/5)x = 4/3
x = (4/3)(5/6) = 10/9.
Implication:
The milk and water solution must be equal to 10/9 of the original volume.
In other words, the amount of added water must increase the volume by 1/9.
Thus, for every 9 liters of milk, the amount of water added = (1/9) * 9 = 1.
Result:
milk : water = [spoiler]9:1[/spoiler].
An alternate approach would be to plug in the answer choices, which the GMAT would provide.
Since price/cost = (5.4)/(4.5) = 6/5, we can simplify the math by letting the selling price per liter = $6 and the cost per liter = $5.
Answer choice: milk : water = [spoiler]9:1[/spoiler].
Cost of 9 liters of milk at $5 per liter = 9*5 = 45.
When 1 liter of water is added, the volume increases to 10 liters.
Revenue from 10 liters of solution at a price of $6 per liter = 10*6 = 60.
(selling price)/(cost) = 60/45 = 4/3.
Success!
The selling price is 1/3 above cost -- a profit of 33 1/3%.
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