In a mixture of 42 kg rice and wheat, the ratio of rice and wheat are `5 : 2`. If 3 kg of wheat is added in the mixture, then what will be the ratio of rice and wheat in new mixture?

Options

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

Answer

To solve the problem step by step, we will follow the instructions given in the question:

### Step 1: Understand the given information
We have a mixture of rice and wheat weighing 42 kg, with a ratio of rice to wheat given as 5:2.

### Step 2: Calculate the total parts in the ratio
The total parts in the ratio of rice to wheat is:
\[ 5 + 2 = 7 \text{ parts} \]

### Step 3: Calculate the weight of rice and wheat
To find the weight of rice and wheat, we can use the ratio and the total weight of the mixture.

- Weight of rice:
\[ \text{Weight of rice} = \left(\frac{5}{7}\right) \times 42 = 30 \text{ kg} \]

- Weight of wheat:
\[ \text{Weight of wheat} = \left(\frac{2}{7}\right) \times 42 = 12 \text{ kg} \]

### Step 4: Add the additional wheat
We are told that 3 kg of wheat is added to the mixture. Therefore, the new weight of wheat will be:
\[ \text{New weight of wheat} = 12 \text{ kg} + 3 \text{ kg} = 15 \text{ kg} \]

### Step 5: Calculate the new ratio of rice to wheat
Now, we can find the new ratio of rice to wheat:
\[ \text{New ratio} = \frac{\text{Weight of rice}}{\text{New weight of wheat}} = \frac{30 \text{ kg}}{15 \text{ kg}} = 2:1 \]

### Final Answer
The new ratio of rice to wheat in the mixture after adding 3 kg of wheat is **2:1**.

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