Two kinds of rice, the first costing Rs. 65 per kg and the second Rs. 95 per kg, are mixed together. Find the ratio in which the 2 types are mixed so that the mixture costs Rs. 83 per kg.

Options

A. `19 :13`
B. `13:19`
C. `2:3`
D. `3:2`

Answer

To solve the problem of mixing two kinds of rice to achieve a desired cost per kg, we can use the method of allegation. Here’s a step-by-step solution:

### Step 1: Identify the costs of the two types of rice.
- Cost of first type of rice (A) = Rs. 65 per kg
- Cost of second type of rice (B) = Rs. 95 per kg
- Cost of the mixture (C) = Rs. 83 per kg

### Step 2: Calculate the differences using the allegation method.
- Difference between the cost of rice A and the cost of the mixture:
\[ A - C = 65 - 83 = -18 \quad (\text{This is a negative value, indicating that C is higher than A}) \]
- Difference between the cost of rice B and the cost of the mixture:
\[ C - B = 83 - 95 = -12 \quad (\text{This is also negative, indicating that C is lower than B}) \]

### Step 3: Set up the ratio using the differences.
- The ratio of the quantities of rice A and B can be expressed as:
\[ \text{Ratio} = \frac{C - B}{A - C} = \frac{83 - 95}{65 - 83} = \frac{-12}{-18} = \frac{12}{18} = \frac{2}{3} \]

### Step 4: Write the final answer.
- Therefore, the ratio in which the two types of rice are mixed is:
\[ \text{Ratio of rice A to rice B} = 2:3 \]