There are two kinds of alloys of tin and copper. The first alloy contains tin and copper such that 93.33% of it is tin. In the second alloy there is 86.66% tin. What weight of the first alloy should be mixed with some weight of the second alloy so as to make a 50 kg mass containing 90% of tin?

Options

A. 15kg
B. 20kg
C. 30kg
D. 25kg

Answer

To solve the problem of mixing two alloys of tin and copper to achieve a desired composition, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the percentages of tin in each alloy and the desired percentage.
- First alloy: 93.33% tin
- Second alloy: 86.66% tin
- Desired mixture: 90% tin

### Step 2: Convert the percentages into fractions for easier calculation.
- First alloy: 93.33% = \( \frac{280}{3} \)% (which is approximately 93.33%)
- Second alloy: 86.66% = \( \frac{260}{3} \)% (which is approximately 86.66%)
- Desired mixture: 90% = \( \frac{270}{3} \)%

### Step 3: Set up the alligation.
Using the alligation method, we subtract the desired percentage from the percentages of each alloy:

- Difference between first alloy and desired mixture:
\[ 93.33 - 90 = 3.33 \]

- Difference between second alloy and desired mixture:
\[ 90 - 86.66 = 3.34 \]

### Step 4: Establish the ratio of the two alloys.
The ratio of the weights of the first alloy (A) to the second alloy (B) is given by the differences calculated:
\[ \text{Ratio of A to B} = \frac{3.34}{3.33} \]

This simplifies approximately to:
\[ \text{Ratio of A to B} \approx 1:1 \]

### Step 5: Calculate the total weight of the mixture.
Let the weight of the first alloy be \( x \) kg and the weight of the second alloy be \( y \) kg. According to the problem:
\[ x + y = 50 \text{ kg} \]

### Step 6: Use the ratio to express one variable in terms of the other.
From the ratio \( 1:1 \), we can say:
\[ x = y \]

Substituting \( y \) with \( x \) in the total weight equation:
\[ x + x = 50 \]
\[ 2x = 50 \]
\[ x = 25 \text{ kg} \]

### Step 7: Find the weight of the second alloy.
Since \( x = y \):
\[ y = 25 \text{ kg} \]

### Conclusion:
The weight of the first alloy that should be mixed is **25 kg**.

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