In what ratio should two qualities of coffee powder having rates of 47 per kg and 32 per kg be mixed in order to get a mixture that would have a rate of 37 per kg?

Options

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

Answer

To solve the problem of mixing two qualities of coffee powder with different rates to achieve a desired mixture rate, we can use the method of alligation. Here's the step-by-step solution:

### Step 1: Identify the given values
- Let the cost price of the first quality of coffee (CP1) = 47 per kg
- Let the cost price of the second quality of coffee (CP2) = 32 per kg
- Let the desired cost price of the mixture (CP) = 37 per kg

### Step 2: Set up the alligation formula
In alligation, we calculate the differences between the cost prices and the mean price (desired price).

### Step 3: Calculate the differences
- Difference between CP2 and CP:
\[ CP2 - CP = 32 - 37 = -5 \quad (\text{Since we are looking for the positive difference, we take } 5) \]
- Difference between CP1 and CP:
\[ CP1 - CP = 47 - 37 = 10 \]

### Step 4: Write the ratio
The ratio of the quantities of the two qualities of coffee is given by the differences calculated:
\[ \text{Ratio} = \text{Difference between CP2 and CP} : \text{Difference between CP1 and CP} = 5 : 10 \]

### Step 5: Simplify the ratio
To simplify the ratio:
\[ 5 : 10 = 1 : 2 \]

### Conclusion
Thus, the two qualities of coffee should be mixed in the ratio of **1:2**.

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