$5$ kg of metal A and $20$ kg of metal B are mixed to form an alloy. The percentage of metal A in the alloy is

### Concept & Formula To find the percentage of a specific component in a mixture, divide the quantity of that component by the *total* quantity of the mixture, then multiply by $100$. $$ \text{Percentage of A} = \left( \frac{\text{Quantity of A}}{\text{Total Quantity of Mixture}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Weight of metal A = $5$ kg * Weight of metal B = $20$ kg * **Deduction:** * Total weight of the alloy = Weight of A + Weight of B * Total weight = $5 + 20 = 25$ kg * **Calculation:** * Apply the percentage formula for metal A: * $\text{Percentage} = \left( \frac{5}{25} \right) \times 100$ * Simplify the fraction $\frac{5}{25}$ to $\frac{1}{5}$: * $\text{Percentage} = \frac{1}{5} \times 100$ * $100 \div 5 = 20\%$ ### Exam Strategy & Shortcut Look at the ratio of the mixture. The ratio of A:B is $5:20$, which simplifies to $1:4$. This means metal A is $1$ part out of a total of $5$ parts ($1 + 4$). The fraction $\frac{1}{5}$ is a standard percentage value that you should have memorized as $20\%$. No calculations are needed. ### Common Pitfall A very common mistake is putting the quantity of metal A over the quantity of metal B, evaluating $(5 / 20) \times 100 = 25\%$. Remember that percentage composition is always relative to the *entire* mixture (the whole), not just the other part. ### Final Answer **Therefore, the correct answer is 20%.**