The ratio in which a man 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. `3:4`
B. `4:3`
C. `2:5`
D. `18:24`

Answer

To solve the problem of finding the ratio in which a man mixes rice priced at ₹10.20 per kg and ₹14.40 per kg to obtain 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
- Price of the first type of rice (P1) = ₹10.20 per kg
- Price of the second type of rice (P2) = ₹14.40 per kg
- Price of the mixture (Pm) = ₹12.60 per kg

### Step 2: Calculate the Differences
Using the alligation method, we calculate the differences between the prices:

- Difference between P1 and Pm:
\[ P1 - Pm = 10.20 - 12.60 = -2.40 \quad \text{(we take the absolute value)} \Rightarrow 2.40 \]

- Difference between P2 and Pm:
\[ P2 - Pm = 14.40 - 12.60 = 1.80 \]

### Step 3: Set Up the Ratio
The ratio of the quantities of the two types of rice can be set up using the differences calculated:

\[ \text{Ratio of quantities} = \frac{\text{Difference of P2 and Pm}}{\text{Difference of Pm and P1}} = \frac{1.80}{2.40} \]

### Step 4: Simplify the Ratio
To simplify the ratio:

\[ \frac{1.80}{2.40} = \frac{1.80 \div 0.60}{2.40 \div 0.60} = \frac{3}{4} \]

### Step 5: Final Ratio
Thus, the ratio in which the man mixes the two types of rice is:

\[ \text{Ratio} = 3:4 \]

### Conclusion
The man should mix the rice in the ratio of **3:4**.

---