In what ratio rice coating Rs. 14/ kg mixed with another rice costing Rs. 11/kg to get the mixture costing Rs. 11.6/kg?

Options

A. `2:5`
B. `1:4`
C. `1:3`
D. `1:5`

Answer

To solve the problem of mixing two types of rice, we will use the concept of alligation. Here’s the step-by-step solution:

### Step 1: Identify the costs of the rice and the mixture
- Cost of rice A (Rs. 14/kg)
- Cost of rice B (Rs. 11/kg)
- Cost of the mixture (Rs. 11.6/kg)

### Step 2: Set up the alligation formula
We will find the differences between the costs of the rice and the cost of the mixture.

- Difference between the cost of rice A and the mixture:
\[ 14 - 11.6 = 2.4 \]

- Difference between the cost of rice B and the mixture:
\[ 11.6 - 11 = 0.6 \]

### Step 3: Write the alligation rule
According to the alligation rule, the ratio of the quantities of the two types of rice can be found by taking the differences calculated in Step 2.

### Step 4: Set up the ratio
The ratio of the quantities of rice A to rice B is given by:
\[ \text{Ratio} = \frac{\text{Difference of B and mixture}}{\text{Difference of A and mixture}} = \frac{0.6}{2.4} \]

### Step 5: Simplify the ratio
To simplify the ratio:
\[ \frac{0.6}{2.4} = \frac{6}{24} = \frac{1}{4} \]

### Step 6: Conclusion
Thus, the ratio in which rice costing Rs. 14/kg is mixed with rice costing Rs. 11/kg to get a mixture costing Rs. 11.6/kg is:
\[ \text{Ratio} = 1:4 \]