Two types of rice of rate Rs. 11/kg and Rs. 21/kg. Find the ratio of two types of rice to obtain a mixture of rate Rs. 17/kg.

Answer

To solve the problem of finding the ratio of two types of rice to obtain a mixture of a specific rate, we can use the method of alligation. Here’s a step-by-step solution:

### Step 1: Identify the costs of the two types of rice
- The cost of Type 1 rice = Rs. 11/kg
- The cost of Type 2 rice = Rs. 21/kg
- The desired cost of the mixture = Rs. 17/kg

### Step 2: Set up the alligation
Using the alligation method, we will subtract the cost of the mixture from the costs of the two types of rice.

- Difference between Type 2 rice and the mixture:
\[ 21 - 17 = 4 \]

- Difference between Type 1 rice and the mixture:
\[ 17 - 11 = 6 \]

### Step 3: Write the alligation
Now, we can write the alligation as follows:

- The difference for Type 2 rice (higher price) is 4.
- The difference for Type 1 rice (lower price) is 6.

### Step 4: Determine the ratio
The ratio of the quantities of Type 1 rice to Type 2 rice is given by the differences calculated:

- Ratio of Type 1 rice to Type 2 rice:
\[ \text{Type 1 : Type 2} = 6 : 4 \]

### Step 5: Simplify the ratio
To simplify the ratio, we can divide both sides by 2:

- Simplified ratio:
\[ 3 : 2 \]

### Final Answer
Thus, the ratio of Type 1 rice to Type 2 rice to obtain a mixture of Rs. 17/kg is:
\[ \text{Ratio of Type 1 to Type 2} = 3 : 2 \]

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