Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

3 : 2 Explanation: The most efficient way to solve this is using the Rule of Alligation . Let the weight of water be . Then the weight of gold is , copper is , and the required alloy is . 1. Apply the Alligation Formula We compare the densities of the two metals against the mean (target) density: Density of Gold ( ): Density of Copper ( ): Target Density of Alloy ( ): The ratio of Gold to Copper is calculated as: 2. Calculation Substitute the values into the formula: 3. Simplify the Ratio Divide both numbers by their greatest common divisor, which is 2: So, the metals should be mixed in the ratio of 3 : 2 . Final Answer To achieve an alloy that is 15 times as heavy as water, gold and copper must be mixed in a ratio of 3 : 2 . The correct option is (c) .

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