In the country, individuals have to pay 20% tax on their income. If the income increases by 25% then the tax rate becomes 140%. Find out by what percentage the amount collected as tax increases?

Let's break down the problem step by step.

### Step 1: Let the initial income be \( I \).

The tax rate initially is 20%, so the amount of tax paid initially is:
\[
T_1 = 0.20 \times I = 0.2I
\]

### Step 2: After the income increases by 25%, the new income becomes:
\[
I_2 = I + 0.25I = 1.25I
\]

### Step 3: The new tax rate is 140%, so the amount of tax paid now is:
\[
T_2 = 1.40 \times I_2 = 1.40 \times 1.25I = 1.75I
\]

### Step 4: Now, we need to find by what percentage the tax collected increases.

The increase in tax is:
\[
\text{Increase in tax} = T_2 - T_1 = 1.75I - 0.20I = 1.55I
\]

The percentage increase in tax is:
\[
\text{Percentage increase} = \left( \frac{1.55I}{0.20I} \right) \times 100 = \frac{1.55}{0.20} \times 100 = 775\%
\]

### Conclusion:
The amount collected as tax increases by **775%**.

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Would you like more details or further clarification on this problem?

Here are 5 related questions to expand on this concept:
1. What happens if the income increases by 50% instead of 25%?
2. How does changing the tax rate affect the percentage increase in tax?
3. Can you find the new tax if both the income and tax rate are doubled?
4. What would be the percentage increase if the income increased by 10% and the tax rate remained the same?
5. How would a decrease in income by 10% affect the percentage increase in tax if the tax rate stays at 140%?

**Tip**: When dealing with percentage increases, always ensure that you're comparing the initial and final values correctly by using relative changes.

Explore how an income increase of 25% and a tax rate increase from 20% to 140% lead to a 775% rise in the amount collected as tax. Step-by-step breakdown, ideal for students in Grades 9-12 learning about percentage changes in real-world applications.

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