A mixture of rise is sold at rs 3.00 per kg. This mixture is formed by mixing the rise of rs 2.10 and rs 2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the mixture if the profit of 25% is being earned.

Options

A. 5:2
B. 2:7
C. 2:5
D. 15:8

Answer

To solve the problem, we need to find the ratio of the price of the cheaper quality rice to the costlier quality rice in the mixture, given that the mixture is sold at Rs. 3.00 per kg with a profit of 25%.

### Step 1: Determine the cost price of the mixture
Since the selling price (SP) is Rs. 3.00 per kg and there is a profit of 25%, we can find the cost price (CP) using the formula:

\[ SP = CP + Profit \]
\[ Profit = \frac{25}{100} \times CP = \frac{1}{4} CP \]
\[ SP = CP + \frac{1}{4} CP = \frac{5}{4} CP \]

Now, substituting the selling price into the equation:

\[ 3 = \frac{5}{4} CP \]

To find CP, we can rearrange the equation:

\[ CP = 3 \times \frac{4}{5} = \frac{12}{5} = 2.40 \text{ Rs. per kg} \]

### Step 2: Set up the alligation formula
Now we have the cost price of the mixture (Rs. 2.40) and the prices of the two qualities of rice:
- Cheaper quality: Rs. 2.10
- Costlier quality: Rs. 2.52

Using the alligation method, we can set up the following:

\[ \text{Costlier Quality} - \text{Mean Price} = 2.52 - 2.40 = 0.12 \]
\[ \text{Mean Price} - \text{Cheaper Quality} = 2.40 - 2.10 = 0.30 \]

### Step 3: Find the ratio of the quantities
The ratio of the quantities of the cheaper quality to the costlier quality is given by the inverse of the differences calculated above:

\[ \text{Ratio} = \frac{0.12}{0.30} = \frac{12}{30} = \frac{2}{5} \]

Thus, the ratio of the price of the cheaper quality to the costlier quality in the mixture is:

\[ \text{Ratio} = 2:5 \]

### Final Answer
The ratio of the price of the cheaper quality to the costlier quality in the mixture is **2:5**.

---