In what proportion may three. kinds of tea prices at 80, 70 and 50 per kg be mixed to produce a mixture worth 60 per kg?

Options

A. `2:2:3`
B. `2:1:3`
C. `1:1:3`
D. `1:3:3`

Answer

To solve the problem of mixing three kinds of tea priced at 80, 70, and 50 per kg to obtain a mixture worth 60 per kg, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the Prices
We have three kinds of tea:
- Tea A: 80 per kg
- Tea B: 70 per kg
- Tea C: 50 per kg

We want to mix these to get a mixture worth 60 per kg.

### Step 2: Set Up the Alligation
We will use the alligation method to find the proportions in which these teas should be mixed. We will compare the prices of the teas with the price of the mixture.

### Step 3: Calculate Differences
1. **For Tea A (80) and Tea C (50)**:
- Difference between Tea A and the mixture: \(80 - 60 = 20\)
- Difference between Tea C and the mixture: \(60 - 50 = 10\)

Thus, the ratio of Tea A to Tea C is:
\[ \text{Ratio of A to C} = 20 : 10 = 2 : 1 \]

2. **For Tea B (70) and Tea C (50)**:
- Difference between Tea B and the mixture: \(70 - 60 = 10\)
- Difference between Tea C and the mixture: \(60 - 50 = 10\)

Thus, the ratio of Tea B to Tea C is:
\[ \text{Ratio of B to C} = 10 : 10 = 1 : 1 \]

### Step 4: Combine the Ratios
Now we have:
- A : C = 2 : 1
- B : C = 1 : 1

To find the overall ratio of A, B, and C, we need to express them in terms of a common quantity for C.

Let’s denote the parts of C as 1. Then:
- From A : C = 2 : 1, we have A = 2 parts.
- From B : C = 1 : 1, we have B = 1 part.

### Step 5: Final Ratio
Now we can combine these:
- A : B : C = 2 : 1 : 1

Thus, the final ratio of the three kinds of tea to be mixed is:
\[ \text{A : B : C} = 2 : 1 : 1 \]

### Conclusion
The three kinds of tea should be mixed in the ratio of 2 : 1 : 1 to produce a mixture worth 60 per kg.

---