X and Y are two alloys of Gold and Platinum prepared by mixing the metals in the ratio of 5:2 and 5:7, respectively. If we melt equal quantities of the alloys to form a third alloy Z, then the ratio of the quantity of Gold to the quantity of Platinum in Z will be:

Explanation

X and Y are two alloys of Gold and Platinum prepared by mixing the metals in the ratio of 5:2 and 5:7, respectively. If we melt equal quantities of the alloys to form a third alloy Z, then the ratio of the quantity of Gold to the quantity of Platinum in Z will be: Solution: Given: Alloy X has Gold and Platinum in the ratio 5:2. Alloy Y has Gold and Platinum in the ratio 5:7. If we melt equal quantities of the alloys, we need to find the ratio of Gold to Platinum in the resulting alloy Z. Step-by-Step Solution: 1. Assume equal quantities of alloys X and Y are melted. Let the quantity of each alloy (X and Y) be 1 unit. 2. Determine the quantities of Gold and Platinum in each alloy: In Alloy X (ratio 5:2): Gold = 5/(5+2) × 1 = 5/7 Platinum = 2/(5+2) × 1 = 2/7 In Alloy Y (ratio 5:7): Gold = 5/(5+7) × 1 = 5/12 Platinum = 7/(5+7) × 1 = 7/12 3. Combine the quantities of Gold and Platinum in the new alloy Z: Total Gold in Z = 5/7 + 5/12 Total Platinum in Z = 2/7 + 7/12 4. Find a common denominator to add these fractions: For Gold: (5/7) + (5/12) = (5 × 12 + 5 × 7) / (7 × 12) = (60 + 35) / 84 = 95/84 For Platinum: (2/7) + (7/12) = (2 × 12 + 7 × 7) / (7 × 12) = (24 + 49) / 84 = 73/84 5. The ratio of Gold to Platinum in Z: Gold : Platinum = (95/84) : (73/84) = 95 : 73 Answer: The ratio of the quantity of Gold to the quantity of Platinum in alloy Z will be 95:73.