In the year 2000, rice formed `20%` of the total food grain production in a country. In the next year, the total food grain production increased by `20%` and the rice production was `25%` of the total food grain production. What is the increase in the production of rice from 2000 to 2001?

Options

A. `25%`
B. `50%`
C. `40%`
D. `30%`

Answer

To solve the problem step by step, we will follow the information given in the question and perform the necessary calculations.

### Step 1: Determine the total food grain production in 2000.
Let the total food grain production in the year 2000 be represented as \( x \).

### Step 2: Calculate the rice production in 2000.
According to the question, rice formed 20% of the total food grain production in 2000. Therefore, the rice production in 2000 can be calculated as:
\[ \text{Rice production in 2000} = 20\% \text{ of } x = \frac{20}{100} \times x = \frac{x}{5} \]

### Step 3: Calculate the total food grain production in 2001.
The total food grain production increased by 20% in 2001. Thus, the total production in 2001 can be calculated as:
\[ \text{Total production in 2001} = x + 20\% \text{ of } x = x + \frac{20}{100} \times x = x + \frac{x}{5} \]
To combine these, we find a common denominator:
\[ x + \frac{x}{5} = \frac{5x}{5} + \frac{x}{5} = \frac{6x}{5} \]

### Step 4: Calculate the rice production in 2001.
In 2001, rice production was 25% of the total food grain production. Therefore, we can calculate the rice production in 2001 as:
\[ \text{Rice production in 2001} = 25\% \text{ of } \frac{6x}{5} = \frac{25}{100} \times \frac{6x}{5} = \frac{6x}{20} = \frac{3x}{10} \]

### Step 5: Calculate the increase in rice production from 2000 to 2001.
Now, we need to find the increase in rice production:
\[ \text{Increase in rice production} = \text{Rice production in 2001} - \text{Rice production in 2000} \]
Substituting the values we calculated:
\[ \text{Increase} = \frac{3x}{10} - \frac{x}{5} \]
To perform this subtraction, we need a common denominator:
\[ \frac{x}{5} = \frac{2x}{10} \]
Thus,
\[ \text{Increase} = \frac{3x}{10} - \frac{2x}{10} = \frac{x}{10} \]

### Step 6: Calculate the percentage increase in rice production.
To find the percentage increase, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]
Here, the new value is \(\frac{3x}{10}\) and the old value is \(\frac{x}{5}\):
\[ \text{Percentage Increase} = \left( \frac{\frac{3x}{10} - \frac{x}{5}}{\frac{x}{5}} \right) \times 100 \]
Substituting the common denominator:
\[ \text{Percentage Increase} = \left( \frac{\frac{3x}{10} - \frac{2x}{10}}{\frac{2x}{10}} \right) \times 100 = \left( \frac{\frac{x}{10}}{\frac{2x}{10}} \right) \times 100 \]
This simplifies to:
\[ \text{Percentage Increase} = \left( \frac{1}{2} \right) \times 100 = 50\% \]

### Final Answer:
The increase in the production of rice from 2000 to 2001 is **50%**.