An alloy contains gold and silver in the ratio 5 : 8 and another alloy contains gold and silver in the ratio 5 : 3. If equal amount of both the alloys are melted together, then the ratio of gold and silver in the resulting alloy is?

Step 1: Understand the composition of both alloys

• First alloy has gold and silver in the ratio 5 : 8
• Second alloy has gold and silver in the ratio 5 : 3
• Equal amounts of both alloys are mixed. Assume 1 unit each for simplicity.

Step 2: Express each alloy in terms of total parts and quantities

• First alloy has 5 + 8 = 13 parts
• Second alloy has 5 + 3 = 8 parts

Step 3: Calculate gold and silver content in each alloy (assuming LCM for equal total quantity)

• Take LCM of 13 and 8 = 104 (to equalize total mass of each alloy)
• Multiply first alloy’s ratio (5:8) by 8 ⇒ Gold = 5×8 = 40, Silver = 8×8 = 64
• Multiply second alloy’s ratio (5:3) by 13 ⇒ Gold = 5×13 = 65, Silver = 3×13 = 39

Step 4: Add gold and silver from both alloys

Total gold = 40 + 65 = 105
Total silver = 64 + 39 = 103

Step 5: Final ratio of gold and silver

Ratio = 105 : 103

Answer: 105 : 103

After melting equal quantities of both alloys, the resulting alloy contains gold and silver in the ratio 105:103.

This question is a good example of weighted average and ratio adjustment commonly used in alloys, mixtures, and metal preparation problems. Understanding how to normalize quantities using LCM makes such mixture questions easier and ensures proportional consistency in combining two different compositions.