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

Options

A. `4:3`
B. `2:5`
C. `18:24`
D. `3:4`

Answer

To solve the problem of mixing two types of rice priced at ₹10.20 per kg and ₹14.40 per kg to achieve a mixture worth ₹12.60 per kg, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the Prices
Let:
- Price of rice A = ₹10.20 per kg
- Price of rice B = ₹14.40 per kg
- Price of the mixture = ₹12.60 per kg

### Step 2: Set Up the Alligation Formula
Using the alligation method, we can find the ratio in which the two types of rice should be mixed. The formula for alligation is as follows:

\[ \text{Ratio of quantities} = \frac{\text{Price of B} - \text{Price of Mixture}}{\text{Price of Mixture} - \text{Price of A}} \]

### Step 3: Calculate the Differences
Now, we calculate the differences:
- Difference between the price of B and the price of the mixture:
\[ 14.40 - 12.60 = 1.80 \]
- Difference between the price of the mixture and the price of A:
\[ 12.60 - 10.20 = 2.40 \]

### Step 4: Set Up the Ratio
Now we can set up the ratio:
\[ \text{Ratio} = \frac{1.80}{2.40} \]

### Step 5: Simplify the Ratio
To simplify the ratio:
\[ \frac{1.80}{2.40} = \frac{18}{24} = \frac{3}{4} \]

### Conclusion
Thus, the ratio in which the man must mix the two types of rice is **3:4**.