The ratio of Copper and Zinc in an alloy is 5: 3. If the weight of Copper in the alloy is 30.5 grams, then find the weight of Zinc in the alloy :

Question

Accepted Answer

To solve the problem of finding the weight of Zinc in the alloy, we need to use the given ratio of Copper to Zinc, which is 5:3. This means that for every 5 parts of Copper, there are 3 parts of Zinc.

Given:
- The weight of Copper in the alloy is 30.5 grams.
- The ratio of Copper to Zinc is 5:3.

Let's denote the weight of Zinc as $ Z $.

According to the ratio, the relationship between the weights of Copper and Zinc can be expressed as:

$$
\frac{\text{Weight of Copper}}{\text{Weight of Zinc}} = \frac{5}{3}
$$

Substituting the given weight of Copper:

$$
\frac{30.5}{Z} = \frac{5}{3}
$$

To find $ Z $, we cross-multiply:

$$
5Z = 3 \times 30.5
$$

$$
5Z = 91.5
$$

Now, solve for $ Z $:

$$
Z = \frac{91.5}{5} = 18.3
$$

Therefore, the weight of Zinc in the alloy is 18.3 grams, which corresponds to Option 4.

**Explanation for why each option is incorrect:**

1. **Option 1 (20.5 g):** If Zinc weighed 20.5 grams, the ratio of Copper to Zinc would not be 5:3. Instead, it would be approximately 3:2, which does not match the given ratio.

2. **Option 2 (20.8 g):** Similarly, if Zinc weighed 20.8 grams, the ratio would not align with 5:3. The calculation would yield a different ratio, not the specified one.

3. **Option 3 (15.8 g):** If Zinc weighed 15.8 grams, the ratio of Copper to Zinc would be closer to 2:1, which again does not match the given ratio of 5:3.

By following the logical steps and calculations, we confirm that Option 4 (18.3 g) is indeed the correct answer, as it maintains the specified ratio of Copper to Zinc in the alloy.