In what ratio must Milan mix two kinds of coffee costing 50rs/kg and 70rs/kg so that the resultant mixture when sold at 72rs/kg yeilds a profit of 20%?

Options

A. a.1:1 `
B. b.8:3
C. c.3:8
D. d.3:2

Answer

To solve the problem of mixing two kinds of coffee costing 50 Rs/kg and 70 Rs/kg to achieve a selling price of 72 Rs/kg with a profit of 20%, we can follow these steps:

### Step 1: Calculate the Cost Price (CP)
The selling price (SP) is given as 72 Rs/kg, and we know that this selling price includes a profit of 20%.

To find the cost price (CP), we can use the formula:
\[ SP = CP + Profit \]
Since the profit is 20% of the cost price, we can express this as:
\[ SP = CP + 0.20 \times CP = 1.20 \times CP \]
Thus, we can rearrange this to find the cost price:
\[ CP = \frac{SP}{1.20} \]
Substituting the selling price:
\[ CP = \frac{72}{1.20} = 60 \text{ Rs/kg} \]

### Step 2: Set Up the Allegation Method
Now we know that the cost price of the mixture should be 60 Rs/kg. We will use the allegation method to find the ratio in which the two kinds of coffee should be mixed.

Let’s denote:
- Coffee 1 (costing 50 Rs/kg)
- Coffee 2 (costing 70 Rs/kg)

### Step 3: Apply the Allegation Formula
Using the allegation method, we set up the following:

\[ \text{Cost of Coffee 1} = 50 \text{ Rs/kg} \]
\[ \text{Cost of Coffee 2} = 70 \text{ Rs/kg} \]
\[ \text{Cost of Mixture} = 60 \text{ Rs/kg} \]

Now we calculate the differences:
- Difference between Coffee 1 and the Mixture:
\[ 60 - 50 = 10 \]
- Difference between Coffee 2 and the Mixture:
\[ 70 - 60 = 10 \]

### Step 4: Determine the Ratio
According to the allegation method, the ratio of the two coffees is the inverse of these differences:
\[ \text{Ratio} = \frac{10}{10} = 1:1 \]

### Conclusion
Milan must mix the two kinds of coffee in the ratio of **1:1**.

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