Question

Gold is 15 times as heavy as water and copper is 7 times as heavy as water in what ratio should these be mixed to get an alloy 13 times as heavy as water?

• A. 1 : 3
• B. 2 : 1
• C. 3 : 1
• D. 1 : 2

Answer 1

Answer:

C. 3 : 1

• The Alligation Rule states that if two ingredients are mixed, the ratio of their quantities is inversely proportional to the differences of their individual values from the mean value of the mixture.

• Let's denote the relative density of the first ingredient (Gold) as C₁ = 15.

• Let's denote the relative density of the second ingredient (Copper) as C₂ = 7.

• The desired mean relative density of the mixture (Alloy) is C_m = 13.

• We set up the Alligation diagram as follows:

  • Place the value of the 'cheaper' or lighter ingredient (Copper) on the left (7).

  • Place the value of the 'dearer' or heavier ingredient (Gold) on the right (15).

  • Place the mean value (Alloy) in the center (13).

• Now, calculate the differences diagonally:

  • Difference between the dearer ingredient and the mean: (15 - 13) = 2. This value goes below the 'cheaper' ingredient side.

  • Difference between the mean and the cheaper ingredient: (13 - 7) = 6. This value goes below the 'dearer' ingredient side.

• The ratio of the quantities of the ingredients (Gold : Copper) will be the ratio of these differences in the opposite order: Ratio (Gold : Copper) = (13 - 7) : (15 - 13).

• This simplifies to 6 : 2.

• Further simplifying the ratio by dividing both parts by their greatest common divisor (2), we get 3 : 1.

• Therefore, Gold and Copper should be mixed in the ratio 3 : 1 to obtain the desired alloy.