The amount of rainfall in Kerala Odisha West Bengal were in the ratio six is to 5 is to 7 in 2017 and in the ratio three is to 4 is 23 in 2022. If in the Kerala, the amount of rainfall is increased by 25% during 2017 to 2022, then the percentage increase in the amount of rainfall in West Bengal during this period is closest to closest to

To find the percentage increase in the amount of rainfall in West Bengal from 2017 to 2022, we can follow these steps:

### Step 1: Define Variables
Let the amount of rainfall in Kerala, Odisha, and West Bengal in 2017 be \(6x\), \(5x\), and \(7x\) respectively.  
Let the amount of rainfall in Kerala, Odisha, and West Bengal in 2022 be \(3y\), \(4y\), and \(23y\) respectively.

### Step 2: Calculate the Amount of Rainfall in Kerala
According to the problem, the rainfall in Kerala increased by 25% from 2017 to 2022.

So, the amount of rainfall in Kerala in 2022 is:
\[
3y = 6x \times \left(1 + \frac{25}{100}\right) = 6x \times 1.25 = 7.5x
\]

This gives:
\[
y = \frac{7.5x}{3} = 2.5x
\]

### Step 3: Calculate the Amount of Rainfall in West Bengal in 2022
The amount of rainfall in West Bengal in 2022 is:
\[
23y = 23 \times 2.5x = 57.5x
\]

### Step 4: Calculate the Percentage Increase
The percentage increase in rainfall in West Bengal from 2017 to 2022 is:
\[
\text{Percentage Increase} = \frac{\text{Increase in Rainfall}}{\text{Rainfall in 2017}} \times 100 = \frac{57.5x - 7x}{7x} \times 100 = \frac{50.5x}{7x} \times 100 = \frac{505}{7} \approx 72.14\%
\]

Thus, the closest percentage increase in the amount of rainfall in West Bengal during this period is approximately **72%**.

Would you like further details or have any questions? Here are some related questions to explore:

1. How would the results change if the increase in Kerala's rainfall were different?
2. What would the ratios imply about absolute rainfall amounts if actual figures were provided?
3. How does the percentage increase in rainfall in Odisha compare under similar assumptions?
4. What would be the effect on the ratio of rainfalls if the percentage change was applied to West Bengal instead?
5. How could this ratio-based approach be applied to other data, like population growth?

**Tip:** Ratios are useful for comparing relative quantities, but always consider whether absolute quantities or percentages are needed for practical insights.

Learn how to calculate the percentage increase in rainfall using ratios. Solve a problem involving ratios of rainfall in different years for Kerala, Odisha, and West Bengal. Understand how to apply percentage increase calculations in real-world scenarios. Suitable for students in Grades 9-12.

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