The ratio in which a man must mix rice at rs. 10.20 per kg and rs. 14.40 per kg so as to make a mixture worth rs. 12.60 per kg.

Options

A. a.4:3
B. b.2:5
C. c. 1.8:24
D. d. 3:4

Answer

To solve the problem of mixing two types of rice at different prices to achieve a desired price per kg, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the Prices
Let’s denote:
- Price of rice A (Rs. 10.20 per kg)
- Price of rice B (Rs. 14.40 per kg)
- Price of the mixture (Rs. 12.60 per kg)

### Step 2: Set Up the Alligation
We will use the alligation method to find the ratio in which the two types of rice should be mixed.

### Step 3: Calculate the Differences
1. Calculate the difference between the price of rice B and the price of the mixture:
\[ \text{Difference 1} = \text{Price of B} - \text{Price of Mixture} = 14.40 - 12.60 = 1.80 \]

2. Calculate the difference between the price of rice A and the price of the mixture:
\[ \text{Difference 2} = \text{Price of Mixture} - \text{Price of A} = 12.60 - 10.20 = 2.40 \]

### Step 4: Set Up the Ratio
Now, we can set up the ratio of the two types of rice based on the differences calculated:
\[ \text{Ratio of A to B} = \text{Difference 1} : \text{Difference 2} = 1.80 : 2.40 \]

### Step 5: Simplify the Ratio
To simplify the ratio, we can divide both sides by the common factor:
\[ \text{Ratio} = \frac{1.80}{1.80} : \frac{2.40}{1.80} = 1 : \frac{2.40}{1.80} = 1 : \frac{4}{3} = 3 : 4 \]

### Final Answer
The ratio in which the man must mix the two types of rice is **3:4**.

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