In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 g of alloy, then the ratio of copper and zinc in the alloy will be

### Concept & Mixture Proportions When a specific quantity of one component is added to a mixture, calculate the initial absolute weights of all components, add the new quantity to the respective component, and formulate the new simplified ratio. ### Step-by-Step Solution * Convert the initial alloy weight to a single unit for easier calculation: $17 \text{ kg } 500 \text{ g} = 17.5 \text{ kg}$. * Initial ratio of copper to zinc = $5 : 2$. (Total parts = $5 + 2 = 7$) * Value of 1 ratio part = $\frac{17.5}{7} = 2.5 \text{ kg}$. * Initial weight of copper = $5 \times 2.5 = 12.5 \text{ kg}$. * Initial weight of zinc = $2 \times 2.5 = 5.0 \text{ kg}$. * Now, $1.250 \text{ kg}$ (or $1.25 \text{ kg}$) of zinc is added to the alloy. * New weight of zinc = $5.0 + 1.25 = 6.25 \text{ kg}$. * The weight of copper remains unchanged at $12.5 \text{ kg}$. * New ratio of copper to zinc = $12.5 : 6.25$. * To simplify, notice that $12.5$ is exactly twice $6.25$ ($6.25 \times 2 = 12.5$). * Therefore, the ratio simplifies to $2 : 1$. ### Exam Strategy & Shortcut Work with fractions or keep decimals simple. Total parts = 7. 1 part = $\frac{17.5}{7} = 2.5$. Cu = 12.5, Zn = 5. Adding 1.25 Zn gives 6.25. $12.5 / 6.25 = 2$. The ratio is $2 : 1$. ### Common Pitfall Adding the 1.250 kg of zinc to the total weight of the alloy and trying to recalculate using the old ratio, instead of isolating the zinc component specifically. ### Final Answer Therefore, the correct answer is **2 : 1**.