A man purchased three types of wheat. Cost of 1st, 2nd and 3rd type of wheat are Rs. `1.27` /kg, Rs. `1.29` /kg and Rs.` 1.32 `/kg respectively. In which ratio are these mixed so that cost of mixture is Rs. `1.30` kg.

Options

A. 1 : 2 : 3
B. 2 : 2 : 3
C. 2 : 6 : 3
D. 1 : 1 : 2

Answer

To solve the problem of mixing three types of wheat with given costs to achieve a specific mixture cost, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the Costs
We have three types of wheat with the following costs:
- Cost of 1st type (C1) = Rs. 1.27/kg
- Cost of 2nd type (C2) = Rs. 1.29/kg
- Cost of 3rd type (C3) = Rs. 1.32/kg
- Cost of the mixture (M) = Rs. 1.30/kg

### Step 2: Set Up the Alligation
We will apply the alligation method to find the ratio in which the three types of wheat should be mixed.

1. Calculate the difference between the cost of each type of wheat and the cost of the mixture:
- Difference for 1st type: |C1 - M| = |1.27 - 1.30| = 0.03
- Difference for 2nd type: |C2 - M| = |1.29 - 1.30| = 0.01
- Difference for 3rd type: |C3 - M| = |1.32 - 1.30| = 0.02

### Step 3: Create the Alligation Diagram
Using the differences calculated, we can set up the alligation:

```
C1 (1.27) C2 (1.29) C3 (1.32)
| | |
| | |
0.03 0.01 0.02
```

### Step 4: Calculate the Ratios
Now, we will find the ratio of the quantities of the three types of wheat using the differences:
- The ratio of the 1st type to the 2nd type is the difference of the 2nd type and the mixture to the difference of the 1st type and the mixture:
- Ratio (1st : 2nd) = Difference of C2 and M : Difference of C1 and M = 0.01 : 0.03 = 1 : 3

- The ratio of the 2nd type to the 3rd type is:
- Ratio (2nd : 3rd) = Difference of C3 and M : Difference of C2 and M = 0.02 : 0.01 = 2 : 1

### Step 5: Combine the Ratios
Now we have:
- 1st : 2nd = 1 : 3
- 2nd : 3rd = 2 : 1

To combine these ratios, we can express them in terms of a common variable. Let’s denote the quantity of the 2nd type as 3x (from the first ratio), then:
- 1st type = 1x
- 2nd type = 3x
- 3rd type = 1.5x (since 2nd : 3rd = 2 : 1, we can express 3rd type as (3/2)x)

### Final Ratio
Thus, the final ratio of the three types of wheat is:
- 1st : 2nd : 3rd = 1 : 3 : 1.5
To express this in whole numbers, we can multiply through by 2:
- 1 : 3 : 1.5 = 2 : 6 : 3

### Conclusion
The final ratio in which the three types of wheat should be mixed to achieve a cost of Rs. 1.30/kg is **2 : 6 : 3**.