An alloy contains tin and copper in the ratio 4 : 5. If the tin has 20% impurity and the copper has 58% impurity, what is the average percentage of impurity in the alloy (approximately)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 41.1%
The impurity of the alloy is a weighted average: each metal’s impurity counts in proportion to its share of the alloy.
Take 9 kg of alloy: tin 4 kg, copper 5 kg
Impurity in tin \(=20\%\) of 4 \(=0.8\) kg
Impurity in copper \(=58\%\) of 5 \(=2.9\) kg
Total impurity \(=0.8+2.9=3.7\) kg
Average impurity \(\displaystyle =\frac{3.7}{9}\times100=41.1\%\) (approximately)
The average impurity is about 41.1%; it must lie between 20% and 58%, which the other options do not.