An anti-friction bronze alloy used in tractor gearbox bushings consists of copper and tin in the ratio $9 : 1$ by weight. If $2\text{ kg}$ of pure tin is melted and homogeneously mixed with $18\text{ kg}$ of this alloy, the percentage of tin by weight in the resulting new alloy is ________ % (answer in integer).
Answer Key:
19
Step-by-Step Solution & Explanation
1. In $18\text{ kg}$ of original alloy:
• Copper $= 18 \times \frac{9}{10} = 16.2\text{ kg}$
• Tin $= 18 \times \frac{1}{10} = 1.8\text{ kg}$
2. After adding $2\text{ kg}$ of pure tin:
• Total tin $= 1.8 + 2.0 = 3.8\text{ kg}$
• Total alloy weight $= 18 + 2 = 20\text{ kg}$
3. New tin percentage:
$\text{Percentage} = \frac{3.8}{20} \times 100\% = 19\%$