Ratio Proportion

[raunakrajan]

In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the "sport" formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the "sport" formulation contains 3 ounces of corn syrup, how many ounces of water does it contain?

Answer 45

[4GMAT_Mumbai]

Hi Raunak,

Standard:
Fl: Corn S: Water = 1:12:30

Sport:
Fl: Corn S: Water = 3:12:180

This simplifies to 1:4:60

If the large bottle has a capacity of x ounces, then

4x / 65 = 3.

So, x = 195 / 4 ounces.

Water = (60 / 65) * (195 / 4) = 60 * 3 / 4 = 45 ounces.

Tricky issues:

How do we figure out 180 in the 2nd line of the equation? It has to be such a number (say p) so that 3 / p will equal 1 / 60. Stems from the question statement that 'the ratio of flavoring to water is half that of the standard formulation'.

Hope this helps. Thanks.

[selango]

Standard formulation

F:C:W=1:12:30

Sport formulation

F/C=3(1/12)=3/12=1/4

F/W=1/2(1/30)=1/60

C/W=F/W/F/C=1/60/3/12=1/15=4/60

F:C:W=1:4:60

C:W=1:15=3:45

45 Ounces of water

[selango]

Shortcut is

F:C=3:12 or C:F=12:3

F:W=1:60 or 3:180

So C:F:W=12:3:180 or F:C:W=3:12:180