In three alloys A, B and C the percentage of copper is` 80%, 75% and 70% `respectively and the percentage of tin is `15%, 15% and 25% `respectively and the remaining is nickel. If 10 kg, 15 kg and 50 kg of the three alloys be mixed together, find the ratio of copper, tin and nickel in the mixture thus obtained.

Answer

To solve the problem, we need to find the ratio of copper, tin, and nickel in the mixture of three alloys A, B, and C. Let's break down the solution step by step.

### Step 1: Determine the Composition of Each Alloy
- **Alloy A**:
- Copper: 80%
- Tin: 15%
- Nickel: 100% - (80% + 15%) = 5%

- **Alloy B**:
- Copper: 75%
- Tin: 15%
- Nickel: 100% - (75% + 15%) = 10%

- **Alloy C**:
- Copper: 70%
- Tin: 25%
- Nickel: 100% - (70% + 25%) = 5%

### Step 2: Calculate the Amount of Each Metal in Each Alloy
Given the weights of the alloys:
- Alloy A: 10 kg
- Alloy B: 15 kg
- Alloy C: 50 kg

Now, we calculate the amount of copper, tin, and nickel in each alloy.

- **Alloy A (10 kg)**:
- Copper: \(10 \times 0.80 = 8 \text{ kg}\)
- Tin: \(10 \times 0.15 = 1.5 \text{ kg}\)
- Nickel: \(10 \times 0.05 = 0.5 \text{ kg}\)

- **Alloy B (15 kg)**:
- Copper: \(15 \times 0.75 = 11.25 \text{ kg}\)
- Tin: \(15 \times 0.15 = 2.25 \text{ kg}\)
- Nickel: \(15 \times 0.10 = 1.5 \text{ kg}\)

- **Alloy C (50 kg)**:
- Copper: \(50 \times 0.70 = 35 \text{ kg}\)
- Tin: \(50 \times 0.25 = 12.5 \text{ kg}\)
- Nickel: \(50 \times 0.05 = 2.5 \text{ kg}\)

### Step 3: Total Amount of Each Metal in the Mixture
Now, we sum the amounts of copper, tin, and nickel from all three alloys.

- **Total Copper**:
\[ 8 + 11.25 + 35 = 54.25 \text{ kg} \]

- **Total Tin**:
\[ 1.5 + 2.25 + 12.5 = 16.25 \text{ kg} \]

- **Total Nickel**:
\[ 0.5 + 1.5 + 2.5 = 4.5 \text{ kg} \]

### Step 4: Find the Ratio of Copper, Tin, and Nickel
Now we have:
- Copper: 54.25 kg
- Tin: 16.25 kg
- Nickel: 4.5 kg

To express this as a ratio, we can simplify the values by dividing each by the smallest value (4.5 kg).

- Ratio of Copper:
\[ \frac{54.25}{4.5} \approx 12.06 \]

- Ratio of Tin:
\[ \frac{16.25}{4.5} \approx 3.61 \]

- Ratio of Nickel:
\[ \frac{4.5}{4.5} = 1 \]

### Step 5: Convert to Whole Numbers
To express the ratios in whole numbers, we can multiply each part of the ratio by a common factor to eliminate decimals. The simplest way is to multiply by 100 to avoid fractions:

- Copper: \(12.06 \times 100 \approx 1206\)
- Tin: \(3.61 \times 100 \approx 361\)
- Nickel: \(1 \times 100 = 100\)

Now, we can simplify this ratio:

The final ratio of copper, tin, and nickel can be approximated as:
\[ \text{Copper : Tin : Nickel} = 1206 : 361 : 100 \]

### Final Answer
The ratio of copper, tin, and nickel in the mixture is approximately:
\[ \text{Copper : Tin : Nickel} = 1206 : 361 : 100 \]