4kg of metal contains 1/5 copper and rest is zinc. Another 5 kg of metal contains 1/6 copper and rest is zinc. The ratio of copper and zinc into the mixture of these two metals :

Options

A. `49:221`
B. `39:231`
C. `94:181`
D. none of these

Answer

To solve the problem, we need to determine the amount of copper and zinc in each of the two metal mixtures and then find the overall ratio of copper to zinc in the combined mixture.

### Step 1: Calculate the amount of copper and zinc in the first metal mixture (4 kg)
- Given that 4 kg of metal contains \( \frac{1}{5} \) copper:
- Amount of copper = \( 4 \times \frac{1}{5} = \frac{4}{5} \) kg
- The rest is zinc:
- Amount of zinc = Total weight - Amount of copper = \( 4 - \frac{4}{5} = \frac{20}{5} - \frac{4}{5} = \frac{16}{5} \) kg

### Step 2: Calculate the amount of copper and zinc in the second metal mixture (5 kg)
- Given that 5 kg of metal contains \( \frac{1}{6} \) copper:
- Amount of copper = \( 5 \times \frac{1}{6} = \frac{5}{6} \) kg
- The rest is zinc:
- Amount of zinc = Total weight - Amount of copper = \( 5 - \frac{5}{6} = \frac{30}{6} - \frac{5}{6} = \frac{25}{6} \) kg

### Step 3: Combine the amounts of copper and zinc from both mixtures
- Total amount of copper = Amount of copper from first mixture + Amount of copper from second mixture
- Total copper = \( \frac{4}{5} + \frac{5}{6} \)
- To add these fractions, find a common denominator (which is 30):
- \( \frac{4}{5} = \frac{24}{30} \)
- \( \frac{5}{6} = \frac{25}{30} \)
- Total copper = \( \frac{24}{30} + \frac{25}{30} = \frac{49}{30} \) kg

- Total amount of zinc = Amount of zinc from first mixture + Amount of zinc from second mixture
- Total zinc = \( \frac{16}{5} + \frac{25}{6} \)
- Again, find a common denominator (which is 30):
- \( \frac{16}{5} = \frac{96}{30} \)
- \( \frac{25}{6} = \frac{125}{30} \)
- Total zinc = \( \frac{96}{30} + \frac{125}{30} = \frac{221}{30} \) kg

### Step 4: Determine the ratio of copper to zinc
- The ratio of copper to zinc is given by:
- Ratio = Total copper : Total zinc = \( \frac{49}{30} : \frac{221}{30} \)
- This simplifies to \( 49 : 221 \)

### Final Answer:
The ratio of copper to zinc in the mixture of these two metals is **49 : 221**.

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